With non-human animals, though, aren't there much fewer possibilities than with humans? Most animals don't have the kind of food surpluses humans have, and so have can't afford to spend energy on things that aren't hunting or gathering food, fighting over territory, or reproducing.

So if an animal is doing something prominently that isn't hunting or fighting or mating or raising young and others are watching but not getting upset by it, mating display is probably a reasonably safe assumption.

I was thinking of extinct animals. (Maybe I should have said "paleontologists".) Whenever there's a structure or physical feature in a fossil whose purpose we can't identify, the default assumption is "it was probably used for mating displays." Sometimes further study (or comparison to extant species) comes up with a more practical use later. It's all hypothetical, of course, but so is "religious purposes." :)

On this note, a vast amount of human energy (surplus and sometimes not, in the aggregate) can be understood as mating displays. Of course, we have added gender to the equation, which complicated things quite a bit.

I'm not sure what the "gender" part of your comment refers to? In the animal world it's generally only animals of one gender (usually males) that engage in these displays.

The means easily becomes the goal for us. Is a dysfunctional mating display still a mating display?