What provides the 'spring' in this mounting system? Is it just the flexibility of the bracket?
Yes. The top-side plates provide the tension. They actually make too brackets, these days, it looks like. The add-on one with a screw in the middle, and the included one like pictured. Their mounts haven't used springs for awhile now.
With a cooler like the Macho, I'd want to make a point of using either desktop-style case, or case with a support bracket, regardless of how it mounts to the CPU, though. That's a great deal of possible torquing.