A telemarketer, in (American) English, is typically someone who makes unsolicited calls trying to sell a product. I would never refer to someone whom I called (by telephone) a telemarketer.
And I would pretty much only ever use the verb "to book" when making reservation (for a hotel room, at a restaurant, or for travel). (Or, in the exceedingly colloquial and probably regional meaning of "get away quickly" (eg, "I booked on out of there")).
So, yeah, this sentence needs some clarification if it actually means something in Norwegian.
Maybe your neighbor is a telemarketer (let's hope not) so they don't need to be trying to sell you something in order for you to overhear them booking a hotel. I agree there should be a note with some clarification, but they put two new words in one short sentence in a way that makes you think, thus making it more memorable. I think the sentence is fine as is.
'What' is the object. It is a strange sentence but not grammatically wrong. It would make sense in a situation where you overhear a telemarketer (whose name you don't know) on the phone saying '8 o'clock, for 4 people' and you wonder what they're booking.
Also I'm English and 'booking' doesn't feel American to me, just a more informal way of saying 'reserving'. I would use 'booking' in the vast majority of cases.