I think the point is that none of these are topology in the mathematical sense. They're computational geometry. In my view that's still one of the most difficult fields of mathematics (precisely because the algorithms rely on extremely complicated data structures), but it's not topology.

If you are groking topology in the mathematical sense, you'd be talking about concepts like (co)homology and homotopy groups, and be doing quite a lot of commutative algebra. You definitely would not care about statistics and point location.