Isn’t “a Catholic lay priest” how you’d best describe the person, in colloquial terms, to a readership that wasn’t familiar with the definition of catechist?
No, I'd define the term. That's not hard to do - especially if you're willing, as the article is, to spot the reader knowledge of the difference between laity and ordination.
To be clear, I'm not OP, and I don't judge the quality of the article on this basis. It's commonplace to see a journalist do sloppy work, especially in parts of an article less critical to its thesis. But the article already defines the term 'catechist', albeit incorrectly. I don't think it's unreasonable to consider that the same trouble should go toward getting it right.
That's not a comparable example. There's a lot more to the priesthood than teaching the catechism - Mass and most sacraments, for example, I believe save only viaticum - and "lay priest" is oxymoronic in any case. To someone knowledgeable in the faith, it sounds like the writer is trying to say "deacon", which would still be wrong anyway, and missing nonetheless; to someone lacking such knowledge, it confers an entirely false impression.
As I said, I think OP makes too much of the phrase, but I agree it's entirely risible.