It's not quite the same. A model is something that you ought to be able to communicate. Theory is something internal, that you can't fully introspect, but you have and you use.

That is doubtless true for the type of people who frequent Hacker News (mostly computer programmers). But in some other communities, the word 'theory' is commonly used in the same manner as Gilbert Ryle uses it. The author of this article is apparently unaware of that fact.

I think the theory encompasses the software itself as an artifact and also the details not included in the software like the problem domain’s details which constrain the software but might not need to be included in the software explicitly.

The model of the software might only encompass the specific ways in which the software is written explicitly, in order to understand how it operates in a near vacuum.

You need a theory in order to reason about a model. The reasoning ability is the important part.