The thing I don't like about "no stress chess" is that the strategy of chess goes out the window, and that's the fun of the game. I don't see what it offers that's superior to using other methods to learn the moves. I also don't see why restricting the child's choice of moves to one type of piece is necessary.
No Stress Chess was DC's absolute favorite game when they were 3 or 4 (now 6 and 8). Now it's standard chess.
Agreed, the strategy for No Stress Chess is very different than a standard chess game, but we weren't looking at it as standard chess, so that didn't bother us.
In our experience with DC when they were 3-4 years old, the restricted choice of moves in No Stress Chess helped a lot. At the beginning, our DC found it overwhelming to look at every possible piece's move, and No Stress Chess gave them the ability to look at the best possible moves they were allowed to make. The other benefits were that it leveled the playing field to some extent, giving them a chance to legitimately win; and they didn't need an hourlong attention span to play. It was also simple enough that DC could interest other kids in playing, too (like at playgroup). That was a big deal here.
Just our experience. YMMV.
