Just stayed there last week, also on a 6 hour stay. Basically, you just book it and indicate your check in time on the booking page on booking.com. It's a bit clunky as the hours they list don't really make any sense, but it's a 24 hour check in. They will message you after booking to confirm in any case and they are responsive through the chat. Agreed that it is annoying you can only do it through Booking and they don't list any contact information.

Overall I thought it was pretty good. Location is great, just off the main concourse, so you can easily go out and get food. Rooms are comfortable and quite big (I booked the deluxe room), although they don't have windows, but not a massive deal. Definitely a good option for a layover and I think decent value compared to the hotel in Doha for example.