There is nothing about the NES that enables Mario's more physics-based behaviour; credit is due to Miyamoto et al for that innovation. Algorithmically, all there really is to it is maintaining a fractional part of location and applying motionuser input as an acceleration rather than directly as a forcevelocity.
So: 16-bit arithmetic rather than 8, two adds rather than one.
The NES has a reasonably fast processor for an 8-bit console but it's within ordinary bounds, and none of the other chips help in the physics calculations.
Sticking with the cost of computation stuff, exact mechanics aside:
Realistic momentum was a key part of the very first arcade game, Computer Space, to the point that few could control it — it's set in space so there's no sense of wind resistance or anything else to decelerate you other than turning your ship around and accelerating in the other direction. You can see that strain of physics get much closer to the mainstream in some of Atari's vector arcade games, Lunar Lander and Asteroids being obvious examples.
A great home example of that line of gameplay is Thrust.
Trying to come up with things that look closer to platformers, and just off the top of my head, Chuckie Egg in its Acorn and Amstrad variations as a title that absolutely nails gravity, and Exile for the Acorns and the Commodore 64 develops a pretty complicated system of physics that also ropes in buoyancy and objects interacting with one another.
I'm sure there are innumerable other examples, many better and/or earlier, those are just some that I'm acquainted with.