When playing zero-sum games (such as most sports or political elections), one can still ask oneself ‘How can all parties win in some other way?’
So, it seems the Christian motivation, in such situations, ought to be to figure out how a non-zero sum game dynamic (‘win-win’) can be constructed.
For example, in a football game, either one team wins or it does not. Yet, all players can grow in character, say.
Zero-sum game dynamics become more acute when looking at politics, where one party wins an election. This can be extended to international politics, where zero-sum dynamics can lead to things like war.
It seems especially important, in these cases, for the actors to try to figure out how to implement non-zero sum games, if not to outright change the game to a non-zero sum game (trade can be such an example in international politics).