Story and Ninja Gaiden in the same sentence doesn't really compute for me. I've put hundreds of hours into these games and I can barely remember what they were about.
It's purely about the combat puzzle. It's about that feeling of being a ballet of blades and stringing combos together from one enemy to the next while dodging and blocking their attacks as effectively as possible. It's about that "flow state" of maximizing efficiency and creating the cleanest, fastest run you can for each level. I have frequently played these games on mute while listening to music or a podcast.