Earlier quoted context omitted.
Netflix and Amazon prime are not TV and don't require a TV licence. https://www.tvlicensing.co.uk/faqs/FAQ104 But indeed, watching any channel on TV (not just the BBC) requires a licence.
I think they make it incredibly clear in their message though: If you’re watching live TV, you need to be covered by a TV Licence: a. if you’re watching on TV or on an online TV service b. for all channels, not just the BBC c. ...
I would think that Netflix and Amazon are considered on demand services.