Slang? Possibly, but you can go anywhere in the UK and ask "What's on the telly tonight?" and people know what you're asking. I'd claim that it's informal rather than regional slang. There's even an L.A. company using it as their name: https://en.wikipedia.org/wiki/Telly_(company)

(I was addressing the parent's claim of 'But English also has no word for "television"')