I disagree strongly. Risk is a great communal game. Lots and lots and LOTS of opportunity to kibbitz, to try and influence others in what they do, etc. I spent one summer on an archaeological field expedition where each evening the Risk board came out and we played until 2 am. Never had a more fun summer.
But it isn’t a strategy game, even a little bit. You can have a strong position one turn, and then a series of bad roles can pretty much destory your position. And the sheer amount of die rolling and counting is just wearying. Good strategy games leave less to luck and more to foresight and planning.
Stranger
Reading reviews of Kemet and Cyclades, they go on my list to get someday. Besides the good-sounding gameplay, I love ancient Egyptian and Greek themes.
I’d recommend Smallworld. It’s a fantasy-based army/territory-expanding game with strategy but very simple mechanics. The unique mechanic is that the forces you start the game with start deteriorating through attrition, and you have to make a strategic decision on when to cut your losses and start again with a new army. There’s a lot of replay value because of the almost infinite number of combinations of races and special abilities.
The last bit is why Chronos is right that Risk is a computer game that got invented too early, not a board game.
But I think you miss the point of Risk. The point of Risk is not a one-versus-one purely intellectual challenge like chess. It’s about maneuvering through the social dynamics of multiple players: allying to take down the leader, scheming someone else into taking down the leader for you, and so on. And also about being able to well, take a risk, and make that big push that, depending on some luck, will let you win the game or ensure you lose the game.
Not the best game for just a father and son. But when there are four or five playing, on a computer so things finish up in under an hour, it’s a great game.
I’m totally onboard with the recommendations for Axis and Allies.
At a lower level, (and not having played it myself but high recommendations from gaming friends whose opinion I trust) is Heroes of Normandie. More tactical than strategic, you can play through many battles from D-day beaches to the hedgerows of Normandy.
For a personal recommendation, I would suggest Game of Thrones: The Board Game, superficially similar to Risk, but less reliant on pure luck. Even without the theme it’s still very much a decent game.
I didn’t disagree with the issue of whether or not it’s a “strategy” game (it is, of course, just not wholly so). I disagreed with your claim that it was better off being some sort of bowlderized computer game that you toss off in a 30 min. drab session of watching on a screen. I find the computer version just as boring as the computer version of Monopoly.
The games that the o.p. describes his son as liking (Settlers of Catan, Star Wars: Rebellion, and Through The Ages) are strategic resource acquisition/management and world building games. These are games where much (or in the case Catan, all) of the gameplay is spent in acquiring and deploying resources in order to put the player in a favorable position when conflict or end-of-game tally occurs. Although there is an element of randomness to these games as well as, at least for Catan, negotiation and barter, the primary focus is learning, adapting, and applying strategies for building and deploying resources and defenses.
Risk is a board game in the sense that it is played on a board, and it is a resource allocation game in the sense that you deploy armies to territories (albeit in a pretty trivial manner since the armies are all homogenous in capability) but in no other way is it comparable to the games the o.p. lists as his son’s favorites in terms of the mechanics of the game in army building and resource management. It is not a game a fledgling boardgamer would take much interest in or play except to accommodate other non-boardgamers.
I’m not really a war boardgamer (I tend to prefer pure resource allocation games like Trajan, or cooperative/competitive survival games like Dead of Winter and Red November, and storytelling games like Machine of Death or player elimination party games like Bang! or The Resistance for social play) so I don’t have specific recommendations for other Axis & Allies-type games, but his son is pretty clearly interested in games with more sophisticated mechanics. I imagine that he’d be bored stiff just rolling dice and smashing armies together, as I know I would be, but the o.p. knows better than anyone what his son would actually enjoy.
Smallworld is an interesting game, and pretty imaginative to boot, but it’s not really a wargame exactly.
I also found Risk to be unspeakably dull; Axis and Allies was better, but still kind of fiddly with all the little plastic counters.
I still think it’s a good suggestion, based off the list given in the op. It’s more of a wargame than Catan anyway. It gives a lot of room for player interaction, allying and kingmaking. It’s a fun game!
I’ll also second the recommendation of Game of Thrones: The Board Game. It really is a good game, even without the flavor.
I agree that Risk is best with six human players, and that (as with any game with more than two human players) politics is a big part of it. But that doesn’t negate what I said. Six people playing on a computer is a lot more fun than six people sitting around a board rolling and counting up ten thousand dice a turn. And you don’t always have six humans: If you’ve only got four, say, then playing a game with four humans and two AIs is going to be better than playing with just the four humans.
Four is marginal; I’d prefer only four humans to four humans and two easy-to-beat AIs. Unless I get to beat the AIs. 
For what it’s worth, there ARE updated versions of Risk with more complicated mechanics, including a legacy version which permanently changes each time you play it. I haven’t personally tried that one but I’ve heard good things.
Thanks again everyone for recommendations.
Risk, at least its original incarnation, is too simple for my son. I’ll let him learn that one at someone else’s house, since it’s undoubtedly a popular game.
Small World looks interesting, but I don’t like the lack of randomness. That amplifies skill level differences, which makes it less fun for my typical conditions. In games with randomness (for example SW:Rebellion) I can tune my attacks so that either one of us can win, depending on dice rolls. Without some randomness, I can’t do that–either I know I win or I know I lose. I’ll hold off on Small World until my son can straight-up beat me (in a few years when he’s in middle school 
).
I’m not a fan of the theme of Twilight Struggle. I feel bad dismissing a game so superficially, but I think there’s enough good games I can get one with a theme I like.
Memoir '44 looks like a great game. I’m not sure it has enough resource/technology development, but not every game has to have that. Assuming he like A&A, I think it’ll make a great follow-on gift. Heroes of Normandie looks interesting, but I think M44 is closer to what we’d like.
Twilight Imperium looks good. I think he can handle the complexity now, but he’s not as into scifi at the moment. On the maybe later list.
Heroes of Normandie is dangerous. It’s a half step away from miniatures wargaming, which you can’t afford to have your son get into. I don’t know your financial situation at all, but trust me, no one can afford it.
See above 
We play Legends of Andor, which is also dangerously close. And my daughter likes that game, too. (She generally prefers games like Settlers of Catan, Seven Wonders, Ticket to Ride, with less direct conflict.) So far only board games, because the physicality helps their focus and imagination at their young age, but I’m thinking about introducing them to an RPG soon. Board games more for analysis; role playing more for creativity.
I thought about recommending TS but refrained because I don’t think your kid would like it based on what you’ve told us. BUT.
Twilight Struggle held the #1 spot on BoardGameGeek across all categories for a very long time. It’s still #1 in the wargame category, though I wouldn’t really classify it as one.
It is an incredibly elegant, incredibly satisfying, incredibly replayable game. I think your disinclination to play based on theme is totally understandable (one of the joys of the game is how strong the theme is), but maybe reconsider it one day. It is one of the most played games in my entire collection, and the single most played 2-player game by a wide margin. I can’t say enough good things about it.
It looks like Target’s entire board game category is currently Buy 2 Get 1. Memoir '44 is on there. So is Risk Legacy, which I mentioned above.
Since this got bumped, I’ll chime in that I saw a copy of Axis & Allies & Zombies at the game store yesterday. I think Avalon Hill is probably most of a decade behind the fad at this point if that’s a new game (I couldn’t find a copyright date on the box). No idea if it’s a good game.
For something more tactical vs strategic, I’d throw another vote in for Memoir '44. It can be pretty high luck as well, though, thanks to the card deck and die rolls.
I’ll put in a plug for Smallworld, as it’s one of my favorite boardgames. While there’s not a ton of randomness, there is some. The combination and placement of races/traits is the big source of randomness, of course; and then there’s the randomness each turn of the single attack roll you can make to gain an extra territory. That single roll would be small in most games, but in Smallworld, a single extra territory can be pretty huge.
I play it with my own daughter, and the ability to talk things through is pretty great. In addition to just chatting about life, we can talk about possible strategy: “Wow, those flying sorcerers look amazing,” I can say. “You’d have to pay an extra three gold to get them, but if you do, you’d be able to use their special ability on any space on the board where I had only a single army.” That sort of conversation is one of my favorite things about board games, and Smallworld really lends itself to them, IMHO.