I disagree with the idea of "taking powers from the GM and giving it to the players" on the basis that it seems to assume that the GM is in a adversial role to the players. But he is not.
The NPCs he controlls are in adversity to the characters the players control.
That might seem like a tiny difference, but it's an important one.
In relation to encounter & monster design:
If anything at all, he is a "trainer" - he challenges the players to do their best, but he avoids demanding too much of them.
The rules are there to gauge whether the things you puts too much demand on your players, to avoid sitautions where, no matter how clever the players are, their characters can't succeed. Or to determine that even if the players don't do anything smart, their characters can't really fail.