Yes, I agree with Nick. It means the person is not 'playing for fun', but 'playing seriously' (with the intention of making the result permanent). Often used NOT in the context of actually playing a game, but perhaps in a business context, where one person is not just messing around or trying to do something, he is DETERMINED and acting aggressively to achieve his aim.
It doesn't always have the dangerous connotation. From the freedictionary: play for keeps
to do things with permanent effect; to be serious in one's actions. (From the game of marbles, where the winner actually keeps all the marbles won.) Are we playing for keeps or can we give everything back at the end of the game?We are playing for keeps, so be careful of what you do.
Playing for keeps means the winner will "keep" the winnings rather than return them at the end of the game. You are not playing strictly for fun.