Simple baseball question as to when precisely a game ends

That sounds like incredibly fast running. As I recall it’s 22 yards you need to run. I don’t recall typical distances to a boundary, nor how fast the ball is going when struck, but, particularly for a six, it’s hard to imagine the ball not passing the boundary before the batsmen were halfway across.

This is similar to what happened in the Harvey Haddix 12 inning perfect game which he lost in the 13th. Felix Mantilla reached first on an error and was sacrificed to second, Aaron walked and Joe Adcock hit a home run. However Aaron, at some point ran to the dugout, I think after he touched second. In any case, Adcock was ruled out, the second out, for having passed Aaron and was given a double. Final score was 1-0. The official scorer at the game had it 2-0, ruling Aaron out and giving Adcock a home run. He was overruled by the National League president.

The difference being that if the runner on 1st fails to touch 2B on the home run, the runner is out, but it has no effect on the batter, unless that was the 3rd out of the inning. But if the batter passes the runner on 1st, the batter is out (and obviously can’t be credited with a home run).