Hey there!
As far as I know, the most noticeable NES restrictions are 3 colours per 8x8 sprite tile, plus transparency.
(There are more that dictate how many palettes you can have and how many tiles you can display at once, but unless you're actually going to put the game on an NES, you don't really need to worry about them).
It's hard to tell how it animates from the stills, would you mind posting it as an animated gif?
One thing I can suggest is adding some upper body movement.
Keep in mind that the term '8-bit sprite' is technically ambiguous, as each 8-bit system had different restrictions, but keeping with the 'vibe' of your friend's sprite and the NES I did a quick paintover of my interpretation of the sprite:
The top one was my first attempt, then I tried it in a couple of other styles that fitted NES colour restrictions, but were further away from the reference image.
Animated:
(It's a bit fast, and could use some fine tuning, but hopefully it illustrates a few of the points I made above.)
Anyway, hopefully this can give you some ideas on making it more 'blocky'
Regards, Scarab