It wouldn't actually change the game very much at all. I bet 80% of games would only be affected by it in the same way that any endgame knowledge affects a game. E.G. Not wanting to make a certain exchange because it will enter into an opposite coloured bishops endgame which you won't be able to convert.
What if the objective of chess
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What if the objective of chess is to get the king to the other side of the board instead of checkmating him?
White king to e8 and Black king to e1