I'd say that the two things that are distinctive to ME are 1. the fluid parkour-like movement and gameplay mechanics and 2. the highly stylized, almost monochrome graphic style, with everything being white or light grey, and only the important objects in bright colors like orange, blue or red (especially the latter). So, how can this be replicated on the NES?
I would envision that the character is animated similar to Prince of Persia and Flashback with the ultra-smooth pixel animations, only with the added mechanic of having the option of not stopping after a jump, but rather chaining different moves and jumps together to seamlessly traverse the terrain.
As for the graphic style, the NES palette is limited, but in this case, this is actually a good thing because it helps bracket the needed colors; three or four shades of white/grey for backgrounds terrain, and two shades of red, orange and blue for the important objects. The key is dithering and shading here, to replicate the occlusion culling that makes the monochrome environment of the original ME pop out.
You feature those concepts in your sreenshots, but I think ther eis room for improvement. The environment could be more muted as outlined above, maybe with even less or more subtle details. The character needs the red/black half gloves on her hands, and for the sprite itself, well, personally I would use Prince of Persia as a reference for realistic human jumping and running poses.
