"If you are trying to learn a translation task — say, English to Spanish, or Images to Text — your model will learn a topology where bread is close to pan, or where that picture of a cat is close to the word cat."
This is everything that topology is not about: a notion of points being "close" or "far." If we have some topological space in which two points are "close," we can stretch the space so as to get the same topological space, but with the two points now "far". That's the whole point of the joke that the coffee cup and the donut are the same thing.
Instead, the entire thing seems to be a real-world application of something like algebraic geometry. We want to look for something like an algebraic variety the points are near. It's all about geometry and all about metrics between points. That's what it seems like to me, anyway.