Actually, check out this clip. The commentary puts it into perspective.
Actually, I would be more impressed if he was on a road in Vietnam and a bunch of buses and scooters were coming at him coming the other way.
As to the OP, the hockey goalie is the one position where when you fail a light comes on to tell the world you failed.
Otherwise, for a boxer to just climb into the ring against some guy that wants nothing more than to kill you has to be stress beyond what most people can comprehend.
Another vote for football placekicker. They’re so good nowadays, everybody just expects them to make every kick, and when they miss, they look like shit.
My first instinct was Closer.
The thing about place kickers is that they aren’t considered real football players anyway, so they’re more outsiders/mercenaries than they are letting down their peers when they botch a kick.
I came in ready to say Hockey goalie, but I’m changing my answer to place kicker. There are season ending Indianapolis Colts losses that I blame entirely on Mike Vanderjagt. Objectively, it’s probably entirely unfair (or at least mostly) but the play at the end is what I remember.
I’d actually lean toward team sports, since you are letting down a group you are part of.
To me it is easily place kicker (though the driver choices has some merit) unless we want get country specific like say North Korean soccer player. Place kickers have to enter the game cold and only get one try. Everyone Else generally gets some leeway to make up for their mistakes.
A cricket captain. Cricket is a game between 22 men, decided in the minds of 2. The one down position, whenever you come in, you have to perform, if their is an early wicket, you have to be the teams recovery man, if there was a good start, well you have to build on that.
Football (the real kind), the Central midfielders, especially the central guy like Roy Keane was.You have to manage the mid field, support the forwards and shore up the defense.
I’d go with pro placekicker also . It’s just assumed you’ll make every one. There is very seldom any praise, just hate. You just almost never hear, “now that was a great kick, great job by the kicker there” unless it’s 55 yards or more or a gale. Hell you even hear praise for the holder(“Great concentration to get that high snap down and turned in rhythm”) than you do for the kicker.
I disagree with the batsman in cricket being the “most high-pressure position”. If you got a first-ball duck and the next player in scores a century, nobody remembers your failure. Maybe the selectors, but you wouldn’t be hassled for the rest of your life, like an American football placekicker who missed the winning kick, or a football player who missed the winning penalty kick. Now that’s pressure.
Another vote here for relief pitcher in MLB.
That was what came to my mind immediately upon reading the OP.
Relief Pitchers have a lot of pressure to be sure but what I think gives placekickers the edge is there are only 16 games in an NFL season making each one count for so much more. Whereas baseball players have so many games to try again that, barring the end of the season, an individual game doesn’t usually mean as much.
Bending over in a squat with your heels off the ground. Lots of pressure on your knees and lower back.
Real answer: NCAA FBS coach
What about football (soccer) goalie? Lots of games are won by a goal and it can’t be easy to have allowed the game winner.
9/10, the stopper had no chance. Of course there are exceptions, see Oliver Kahn 2002 World Cup Final.
Serious question: how active is a soccer goalie? How many shots/chances is he facing? His role is similar to that of a hockey goalie, but a hockey goalie is expected to stop 20-30 or more shots that are pretty much guaranteed goals. I don’t watch a lot of soccer, so I don’t know if their goalies are facing something similar in terms of stress/saves.
My hesitation with agreeing with a placekicker as being the most stressful position is only that so many kicks aren’t necessarily game winners - is the stress just as high when you’re up by 10 as when you’re down by 3? I agree that kicking on the last play of the game to win it all is probably one of the most stressful moments in sports, but is the kicker more stressed on average than a quarterback or hockey goalie or other suggested player?
Semi-related: I often tell my husband that I’d love to see a live heart rate monitor (or other vital sign tracking) on a goalie during a hockey game; the intensity of a goalmouth scramble or of a quick glove save on a point shot must be crazy! I’ve never thought about it much for other players in other games, but that’s only because I’m more of a hockey fan and love goalies 
I can’t see that a place kicker or hockey goalie can possibly be under more pressured than a football keeper. Bear in mind that the worth of each individual goal in football is more than in either of the other two sports and so the individual cost of a cock-up is more for a football keeper.
That’s all true and I see your point, but the problem I see is that it is rare that a gaff by a goalie will cost a game in the closing seconds. Sure, a goalie mistake WILL cost them the game but not necessarily at the end. When a game is tied and they go to penalty kicks the goalies don’t generally receive any of the blame. For a kicker, the game is on their foot in the closing seconds on a remarkably regular basis. Heck, this weekend in college football I can think of 2 just off the top of my head (and I’m sure there were more).
Another vote for F1. Individual and not a team sport, beaucoup buck, worldwide attention and a moment’s lost concentration and you get maimed or killed. The worst a placekicker has to face is tearing up his knee celebrating.
Field goal kicker was my thought. Being widely despised for your clean uniform, you’d better at least do the job when called on, which is often a win-or-lose moment.
Soccer goalkeeper.