Specifically, section 6 (Compuation and Waterfalls), which gives the answer that System X computes Y whenever it saves you the work of computing Y -- i.e. if being able to use X as an oracle decreases the asymptotic difficulty of Y.

So waterfalls (probably) don't play chess in the sense that any mapping form the waterfall to a chess program would itself be as complex as the problem (and its execution). But a chess computer does, since its output has a very simple mapping to actual moves (and in practice, most chess computers add a view layer to provide that mapping transparently).