[p1mrx]

Reminds me of Uncle Worm, among the better TI-83+ games. It's 2D, but the snake is curvy:

https://www.ticalc.org/archives/files/fileinfo/96/9683.html

[westurner]

That says 2004.

Snake (video game genre) https://en.wikipedia.org/wiki/Snake_(video_game_genre) has a picture of Hyper-Wurm on a TRS-80, which looks curved or spherical

Is there already a Snake on a Plane?