I noticed in both the video game Shinobi and Strider the ninja character wears a red scarf. Is this a reference to something Japanese?
Apparently (going by a post on this Reddit thread) it is a thing from ninja folklore:
(Also mentions that in manga/anime/games having the scarf helps in being able to suggest fast movement in the character.)
There’s A Trope For That, but no explanation.
(It really doesn’t help in searches that apparently “ninja scarf” is a type of hijab.)
Visually speaking it does suggest speed and looks really cool. So that’s probably the main reasons.