Apparently I misremembered slightly: it's actually width + 2 x length + 2 x height.

That link doesn't seem to explain the why, but my understanding is that it's just a decent heuristic for the general difficulty of handling packages as they go through the system. Volume wouldn't be appropriate, because a really long, skinny box is harder to handle than a cube of the same volume.

How do you decide which dimension is the width versus the length? I assume height is often significant for packages containing things that shouldn't be turned upside down, but length versus width seems pretty arbitrary. Is width just assumed to be the shorter of the two dimensions?

Length is defined as the longest side. The other two sides are interchangeable so pick what you like. This measure doesn’t appear to account for packages that require a certain orientation.