Obviously you should not be rotating, but finding features of the shapes that are invariant with respect to rotation to calculate. We can think of the two middle segments as defining two coordinate axes which I'll just call the body, with the remaining segments the legs. There are three cases. 1) both legs coplanar with body: W, question mark, and O. 2) neither leg in the plan of the body: The lightning bolt, and the forklift. 3) one leg coplanar with body: Z with leg, Hook with leg.
Unfortunately, the lightning bolt, Z with leg, and Hook with leg are all chiral, (and are therefore more likely to appear, reducing the effectiveness of this heuristic), but just guessing among matching classes is sufficient to get 20 matches. A quick test of chirality could maybe do better, but I suspect it's most just about speed of guessing after this.
edit: 32 is my high score after playing for an hour. Which is at least higher than the brute force clicker guy's score, so I feel like I can be done. The human brain is very good at optimizing its solutions to this problem.