Maybe I'm wrong, but I think there is confusion here over the CCTV image and the last sighting - they aren't the same thing. There isn't footage of her 'going in but not coming out' of a hotel, there is footage of her at a big entertainment complex, and then a further sighting later on the same night at a hotel round the corner. There isn't CCTV footage of her entering that hotel, this must be based on witness statement. Perhaps the man who they have been questioning has admitted he was with her at the hotel. I'm guessing that CCTV image is the last actual evidence they have found of her so far, possibly in that image she is leaving the SKY entertainment complex and the next time they pick up her trail is at the hotel. I'm going by that image recreation from the newspaper that someone posted.
Possibly they do have further CCTV but are holding it back. Or the hotel in question doesn't keep its CCTV past a certain date, if it has any. Sometimes they wipe after 24 hours and she may not have been reported missing in time to catch it. This could also be true of other venues in the entertainment complex.
Would they do a search of the whole hotel building without 'reason to believe that there is foul play'? Surely it would disrupt the running of a hotel which they aren't likely to do unless they have a lead. A missing adult, however out of character, wouldn't usually lead to a forensic search would it, unless there is an actual suggestion of her having been murdered?
As someone else has pointed out, the family say she was in touch daily. But she didn't contact them after Thursday, even though we know she was alive and well on Saturday. So it had stopped being 'daily' before she officially went missing.
I know it is the age of ultimate connection, and of course there is plenty of reason to be worried, but is there also reason to be optimistic? When I was young, and people went travelling, you wouldn't expect to hear from people every day. Or even every week. A phone card call from a call box once every so often and an air mail letter would have been plenty of contact. Maybe this young woman just needs a break from family responsibility and didn't realise that it could cause such an uproar? Her father is rich and therefore potentially influential, and the family have done an expert job of raising awareness via social media platforms. It could be that all this is as much of a driving force behind the swift police action as actual concern.
I don't know. Maybe wishful thinking. I desperately hope she is ok.