Team implies more or less equal/comparable competitors playing the same game. Class implies a class-based system like castes that assigns your worth, identity and role based on which class you're in. I think the switch to classes is quite apt and clever.

Overall, I finally felt I understood the article when I considered it in the context of US politics. It seems like a very pointed article addressing a very specific issue. It's trying to avoid being interpreted as a political message where people will automatically take sides based on their political affiliation, which is why the author is intentionally vague.