Author here! If a group of people use a word and also all understand what others in the group are saying when they use it, then the word does in fact mean what they think it means :)

I have no math background but can read ancient Greek pretty fluently. “Isomorphic” is simply a Greek compound word meaning “same shape.” The reason people use “isomorphic” for server side rendering + hydration is that you can create an application where all the components have the “same shape” in various ways (i.e., the same source code, arguments, templating, etc.)

A technical term having a different meaning in two different fields doesn’t mean that the version with which you’re more familiar is correct and everyone else is wrong. That would be like commenting on an article entitled “Syrian rebel forces take Damascus” to say “National-security people keep using the word ‘forces’. I don’t think it means what they think it means. To me, force equals mass times acceleration.”

That's such a silly analogy it's tantamount to constructing a straw man.

I don't have a background in mathematics either, but I think it's quite clear that the use of "isomorphic" here as a stand in for code sharing is forced, to say the least.

It's the same kind of silliness as using the term "tree shaking" in place of dead code elimination (which is, you know, an established technical term in the same field). In this instance however, instead of using a fancy-sounding word (which I think is a little pretentious), they've gone with an analogy with a less obvious meaning (what are you shaking from the tree? Are the good bits falling off also?).