Does that mean I owe a license fee for YouTube? Am I obliged to check before every video?
(Obviously these are ridiculous hypothetical questions, and I don't expect answers, but the policy itself is ridiculous)
I don't think the policy is that ridiculous, it's just that it's one of these where certain edge cases like this one can be safely ignored. You will be tracked and found if you use the BBC iPlayer without having paid the licence, you will not be found out for watching some random live youtube channel. It's an imperfect rule for a complex world.
Sky offer a streaming service in the UK called NowTV which includes live TV streaming of their channels, as well as Netflix-style on-demand streaming from their library. They're very upfront that a TV licence is needed if you wish you watch their live channels over NowTV, [0] but one is not required for on-demand streaming.
[0] https://help.nowtv.com/article/do-i-need-a-tv-licence-to-wat...
If it's broadcast simultaneously by other means (e.g. satellite, cable, terrestrial transmitter etc.) it counts as "live TV".