Do I get it right that the goal is to be the last player to cash out right before the game "crash"?
What would prevent the site owner to play himself, since he knows the gameCrashAmount and could act as a lucky winning player (effectively a shill)?
You're right that that is the goal, but it's not all that important.
Everyone who cashed out before the crashpoint gets paid their stake times the multiplier when they cashed out. So if the house was to cheat and make sure they're the last to cash out, they wouldn't be making you lose.
The only caveat to that is that the last player to cash out gets the bonus, which is 1% of the total staked on that round. (It's not quite that simple, because you don't want a player making dust bets to be able to scoop the whole bonus, so the amount each player is eligible to win is scaled down in proportion to the size of their bet in comparison to the size of the biggest bet that round, with the rest of the bonus pool being awarded to the next player in reverse cashout order). So the best the house could do is win that extra 1% each round.
Skillful players will aim to win the bonus, and only play when they have a positive expectation. If the house was cheating in the manner you describe, it would no longer be possible for skillful players to have a positive expectation, and the house edge would then be between 1% and 2% for them.
In short I don't think this is a very good way for the house to cheat. They'd be better off just making the game crash early more often than it should. We currently have to trust that they don't do that.