> So when X is a model of Y, then Y is always also a model of X?

Yes.

> That seems like a strange definition of “model”.

Yes, it does, but I can defend it. It's analogous to the definition of "information". If a system X contains information about a system Y then it is always the case that Y also contains the same amount of information about X. The distinction between "model" and "modeled" is purely artificial in the most literal sense: the thing we generally label "model" is the thing we humans made.

I agree that this is a problem with the above definition of model, analogous to the (IMO fatal) problems with https://en.wikipedia.org/wiki/Deductive-nomological_model#We....

That has to do with causality, which is a complicated topic that I was trying very hard to avoid at this point in the exposition. But maybe that was a mistake.