Just checking some career stats here.
46 games
passing: 10/18 for 205 yards, 0 TD 1 INT
rushing: 98 for 538 and 4 TD
receiving: 28 for 312 and 7 TD
So he runs the most, catches the second most, and throws the least. That doesn't sound like a QB to me. No other QB I can think of runs and catches more than he throws.
Clearly the most accurate way to describe him is, he's a hybrid player that doesn't fit neatly into any of these boxes. But gun to my head, I'd probably label him a RB. The fact that he takes direct snaps doesn't make him a QB. Lots of RBs were taking snaps back when the wildcat was all the rage. That didn't turn them into QBs. TE would be the next option I'd pick, followed by WR. QB would be the last option/least accurate label.