Ahh okay I think I get it now, you are saying if chess is win for black, that immediately implies zugzwang for white from starting position.
In the same way, chess being a win for white implies zugzwang for black starting position.
So chess being a win for one side is equivalent to starting position being zugzwang for the other side.
It's obvious now, but so interesting to me, I never thought about it that way! Thanks for taking time for explaining yourself.
White could win without zugzwang!
Because white starts. After the first move, the position is no longer symmetric, so it doesn't help black to skip to switch sides.
