Pedantry is okay. I make a fair living doing it. And, I must admit that I've probably heard "fixed wheel" more than "fixed gear" in the past; but I wasn't counting. For the most part, however, people would simply use the term "fix" to describe the bike they were riding.
I'm not sure that "fixed gear" is inaccurate, though "single fixed" gear might seem redundant, except to those who have (or have heard of) "multiple fixed gear" hubs. It seems, to me, that it's the system (rear wheel and gear) that is fixed, given that while riding neither is variable.
Anyway, I guess "fixie" sounds like a diminutive for "fix." But, I won't pull out my remaining hair over it.
Steve James
Bronx, NY USA