Why is it OK for angels of God to influence the outcome of games? Why couldn't God detect the sarcasm of Roger's dad's fateful words?
It's a "kill two birds with one stone" thing. The angels influence the outcome of relatively meaningless games (not influencing games that had major repercussions with one exception) to have the coach feel genuine affection for Roger & JP, leading to both of them to get a good home, as well as make the coach a better person and provide a Magic Feather for The Team. As for The Needs of the Many, the good book says "Ask you shall receive". Roger asked and, as far as we know, no one else did. God knew that Roger's dad was being sarcastic but Roger didn't pick up on it.
Part of it is also the fact that Roger asked in a very distinct way from the way most people ask God to help a team win. Most people just want the team to win because they like the team or they feel it will give them bragging rights over fans of other teams or they want to win money. Roger asked for the team to win because he sincerely wanted his father back. Thus there is now a less selfish and multi-layered reason for God to do this. 1) It accomplishes the above points of helping all the various people on the team improve their lives and feel better about themselves and others, 2) it gives Roger hope, and 3) it gives Roger's dad a chance to make good on his (sarcastic) promise and become a better man (even if he chose not to do so, but then that's a consistent aspect of stories like this, God can offer the opportunities but it's still up to people to make good on them).