Because the algorithm is called minmax, no? Alpha-beta pruning is an optimization.
I have collected some statistics. I do get cutoffs. The number of cutoffs is roughly 4% off the total examined nodes. What does that actually mean, though? I really have no idea. Since I don't count the total nodes when getting a cache hit and I don't know how many nodes are cut off from the alpha-beta, I cannot count how many nodes are actually pruned.
But this ordering... I'm afraid I don't know why it would help or how it works.
It is just my first AI algorithm.