QTM is a metric for, well, counting how many moves a sequence of moves really is. 1 move in QTM is a single quarter turn of one of the outer layers of the cube (so F, B, U, D, R, L). So double/half turns such as R2 count as 2 moves in QTM (compare with HTM (half turn metric) where R2 is counted as one move). Inner layer turns such as M count as 2 moves as an M move can be achieved by performing R and L' and then rotating, which itself is 2 moves. Note rotations in QTM do not count as moves.
In regards to the actual test, personally it appears to be more of a 'cubing trivia' than a 'cubing theory' test. As mentioned before, most of the questions are biased towards CFOP solvers, some of the questions are subjective (e.g. how to get sub-15), and some have nothing to do with actual cubing 'theory' (e.g 2x2 WR). Don't get me wrong, the idea is cool, and could be really great once the idea is fleshed out with some more questions (for instance when I first saw 'cubing theory test' I was low-key expecting things on Group Theory, commutators, etc, but ah well.)
