I use "CPU" as "nonspecific entity that supposedly controls everything other than your character(s) in a game, including puzzles, npcs and furniture", out of habit. I forget the common meaning for that word is for bots controlled by the game.
Also, it's a game, and games end with someone winning and someone losing, because the first beat the second. Since we
play games instead of simply "going through" them, it seems like a gamey term like
beat is more adequate, for coherence.
Cardinals end five-game losing skid, beat Giants 5-1
In a single player game, that someone else would be teh evul CPU. "Finish" makes me think of something non interactive, like a book, but I also use it for games just as much, also out of habit.
I dont have a "incorrect" word for it since I grew up hearing all sorts of terms, including something that in english is like "turning over" (because you go back to the intro screen after reaching the ending, that is, the game turns over, hur hur) and "zeroing" (because the score would eventually revert to zero after you accumulate an obscene amount of points, also used for games without a score by osmosis)
As for "beating" adventures, it's because your objective is to reach the ending, like always (at least, an ending where you don't die horribly), despite gameplay consisting of puzzles instead of bot-mashing.
Then again, like CreamyBlood said this is so minor and irrelevant, it's hilarious, so have some of
this to lighten the mood.