The Romulan War was 2155-2160, Discovery is an old ship but she's operating in 2255. She's in an asteroid base because both she and that teaser were based off a piece of concept art from around the time of TOS's production showing the ship inside such a base. That's all.
Trek has 50 years of history accumulating canon like a rubber band ball. Just because something wasn't part of the original plan (and some of those races didn't exist in TOS) doesn't mean you can't draw a connection later and embrace it as part of the universe. That's how creativity works sometimes. Happy accidents and serendipity.
I never said you couldn't do any of that. I said that I felt they were reaching with their "hypothesis" that the major Trek aliens represented the 7 deadly sins. You know, like when an author takes something out of context to fit with the story they're trying to tell (cough, cough, Andorian sexes, cough)
"Kilkenny Cats", which from all I've read sounds like it was basically DS9's "The Abandoned" with a Kzin instead of a Jem'Hadar.