But it is available on Google video here.
“Tea, girls…warm and so sweet,
some’r set up in the Somerset Maugham suite”
(Two “summersets”, get it?) 
That should read, “…some’re set up in the Somerset Maugham suite.” (Might make a little more sense that way.) 
Also, “Get Thai’d! You’re talking to a tourist
Whose every move’s among the purest…”
Pretty clever lyrics (by Tim Rice) couched in that cheesy little song.
I think John Fogerty was talking about Strat-o-matic.
Tim Rice & ABBA did Chess; Andrew Lloyd Webber & Ben Elton did football (or, as we Yanks call it, soceer) in The Beautiful Game. Check out the title song “Viva The Beautiful Game.” I first heard it during the Subway Series and did a parody “Viva The Yankees and Mets.”
I think the classic Zeppelin song “Pretty Sneaky Sis” was about Connect Four.
Oh, bravo. Bravo.
How’s about anything by Fats Domino or Chubby Checker? (To tie this to the OP, the latter purposely chose his stage name to have a game it in, like the hugely successful former.)
Thank you! I could never figure out what that line was!
XTC’s “Happy Families” (it’s a board game popular in the U.K.)
“…It starts out with a dealing in the middle of the night/And ends up with a full house if you play your cards out right…”
Glad I could be of service. 
If electric train racing counts, then the whole cast recording of “Starlight Express.”
AC/DC’s sin city:
“Ladders and Snakes
Ladders give
Snakes take.”
Chris Cornell’s “You Know My Name,” the opening track to the recent Bond remake “Casino Royale,” has several lyrics that are indirectly about poker, but are ambiguous enough to mean just about anything.
Okay, maybe I have no taste, but I don’t think the song is either cheesy or kitschy.
If you would consider sports - Big League - Tom Cochrane?
I feel obliged to bring up this wonderously inventive and humorous (ahem) thread on this subject already. 
Searching the Archive, Guy?
I didn’t think of Pinball Wizard from Tommy.
I submit Chuck Berry’s My Ding A Ling
That makes two of us. I think the lyrics are tremendously clever faux double-entendre. The only other writers to incorporate such complex and funny plays on words were Gilbert & Sullivan.
Motorhead’s “Ace of Spades” is all about poker.