We play would be better, and more natural instead of we game.
But then it´s music. Poetic licence and all that.
As for Me-we, I sit on the fence.
Yet, outside of music I wouldn´t use or suggest it. Grammarians would say that "me and we'' (sic) makes "us''.
It would even impossible to say "I" and "we" too, so "US" is the word.
But it´s music!