But it seems to me, maybe naively so, that most of my human abilities involve massive amounts of number crunching that no desktop computer could do.

I think it's an unfair comparison because you are allowed to cheat. You don't have to produce 1500×1000 pixels, 25 times per second, consistently, with correct lights and reflections, etc. Different minds may work differently, but I suspect there is a lot of cheating. A bad result may seem OK, because you are allowed to fix any detail at the moment you start paying attention to it; you don't even have to notice that you are doing this.

On the other hand, it wouldn't surprise me if human brain would be really faster in some tasks -- those we are optimized for by evolution, such as image processing. Visual part of brain does some massive parallel computation, and if a task allows parallel computation, many slow computers can outperfom one fast computer (or a smaller group of fast computers).

Both effects may work together -- we have parallel hardware optimization for image processing and we are allowed to give imprecise answers and even cheat.