The Atlantic article (which I'm obviously not the target audience for, I find them hard to read with all their side stories and presenting n=1 anecdotes as meaningful) seems to not argue about the idea that they are markets, but rather that we shouldn't consider them as markets when we are engaged in it, i.e. if you're having a good time with A, you shouldn't wonder whether you could have had a slightly better time if you had met with B. Don't treat your friendships as you might buying a cell phone. Even business relationships have shifted in that direction, in my experience, it's a pretty recent thing to "shop around" and switch providers because you might save a few bucks.
That's a different issue though, I don't believe that's happening because economists or sociologists use market-models to analyze relationships. Tinder and the commoditization of dating, like-count-fetishizing etc are not a thing because somebody said "hey, you know how car sales work? we should manage our relationships that way". Rather, it's how humans work on a very low level and these technologies and trends are just exposing that by giving people a way to visibly act on it. This isn't new, and pointing it out doesn't cause it, neither will it vanish if we just don't mention it and pretend it's not real.