Which is also a definition that aligns more with the show because the Avatar is essentially the current in a long line of reincarnations of a god-like being who can bend all four elements. The blue avatar refers to using technology to allow humans to inhabit/control a digital or physical being.

Though I think a lot of people in the West wouldn’t automatically think of either show or movie if “avatar” is used in the context of “an avatar of x” or “my avatar jumps when I hit spacebar”. Some might not know what you mean, but it’s probably enough context that they don’t think it’s the show or movie (or movie about the show).