It is a bit strange that this website gives bitcoins as cash back, but doesn't allow users to book hotel rooms using bitcoins.
Do they actually buy bitcoins which they give to the users?
The reason is simple. They do not process hotel bookings themselves, but are an affiliate of booking.com. They receive a commission of up to 8% or so (as far as I remember), and will return a portion of that to the person who made the booking. Since they receive their commission as an affiliate in EUR or USD, they obviously have to buy the BTC for the cash-back to their customers somewhere.