Providing a direct answer is a little tough because of your obscure case, but I'll attempt to provide a few thoughts:

From your example, I wouldn't necessarily agree that the GameInningDim and TeamDim dimensions can be combined. I would rather want to combine the GameDim and GameInningDim dimensions, as those dimensions seem to be directly related but at a different grain. This would of course only be possible if the duration in the GameFact can be expressed by innings.

Assuming it is (expressing the duration by innings that it) and that you have an InningDim dimension, you could maybe even do without the GameInningDim and use the fact to create the association between the Game, Inning and Team dimensions.

Hope this helps...