All my answers presume the game has a definite outcome of win or lose depending on how you play the game.

It would not bother me to win - because we all have our own skills an talents. I wouldn't "let" the other person win because it would cheapen the victory.

It would make no difference to me if someone I was trying to impress were watching. I'd desire to do my best, win or lose.

I would go on playing even if being watched.

Of course it would depend on the game - but any game where you have a definitive outcome (Trivial Pursuit, Scrabble, or the like) I am going to do me best.

I can't help but thing a better question, overall, might be - do you fear what impression you make if you can beat an opponent soundly and easily?