Not so much "outside his skill class" as "unlikely to be played by a human". Computers have a really good idea of what the optimal move is, and it's sometimes not a move any human being would play. The main way to detect cheating is to figure out that they're playing closer to the computer's line than anybody without computer assistance.

In this case, his off-the-board behavior, where he seems unable to explain some of the moves he made, is also suspicious. His skill set is such that there's no move he's not capable of playing, though he should at least be able to tell you what he was thinking when he played it.