Earlier quoted context omitted.
Pedants* like you. Everyone knows what chai tea is referring to. In the same way they understand what naan bread is.
Doesn’t mean it’s correct!
Still, rude to correct someone for using what's essentially a colloquialism. If enough people use a word 'wrong' then, well, that's a new usage that we can't ignore or get prescriptive about. Because prescriptive usage is from some point of view after all. The Chai tea people have their point of view, and are correct within their community.