I don't think he explained it well, but what actually makes a show/manga/game "chuuni" is usually the presentation. It's kinda derogatory in the same way as how some people tend to look down comic book or videogame style works in the west which try super hard to be taken seriously.
When you have something like Naruto or One Piece, where it's clearly targeted at kids and not trying to be anything more, that's not really chuuni because it knows what it is. But when you have those same elements but in a more "serious" context where the authors clearly seem to be taking everything seriously even though it has ridiculous stuff like "The 5th Holy Grail War" and all sorts of made up "rules" and characters shouting attacks while doing them, that's definitely what people would call "chuuni". That also includes all sorts of references to "cool" stuff like [The Mage Association] and so on. It's just viewed as very childish manchildren stuff. Yes, stuff like Xenogears and FFXV are totally viewed that way too.
I guess one parallel in a western context would be the term "syfy". It doesn't mean the same thing, but in cultural tone it's similar in the sense that it's a critique by viewers comparing actual scifi works which are approached in good faith, and scifi works which are just pandering dumbed down stuff meant to hook dumb audiences with superficial presentation and garbage worldbuilding which relies on twists and poorly thought out but cool sounding stuff. Oh, and I guess "phantasy" works the same way too.