Comment by vunderba
I think noteworthy is the key. Others with tight controls and timing that I can think of (that are less known) are Downwell, Caveblazers, Celeste, Super House of Dead Ninjas, Tiny Barbarian DX, VVVVVV.
And these are just ones that I've personally played.
I have heard of Celeste and I have played through VVVVVV. I will check out the others.
Celeste is kind of an example of what I was talking about though. The game gives you a ton of movement options and "floaty" air control with a lot of maneuverability. NES games never did that. The controls were simple and highly responsive, but generally very "committal."
The only recent game I know of with controls that really felt like a NES game was La Mulana. That game did not allow you to reverse directions in the air after a jump. Once you jumped forward you were fully committed to the arc of that jump.