It's on sale. Just bought original AITD 1-3 trilogy. Is New Nightmare worth playing?

I would say yes.
Objectively, it's a decent Resident Evil clone, does nothing amazing or particularly superior to every other RE clone (or RE itself) to stand out of the lot.
Personally, i'll always have a special place for it because it was one of the games that introduced me to the horror/survival horror genre, one of my favorite genres still to this day.
Give it a shot, it's a cheap game anyway, just don't expect it to amaze you.

It's actually the other way around - AitD inspired RE. Particularly the adoption of the fixed-camera angle.