What does this mean? Is the price per person? If so, does that mean a double room is twice as expensive as a single room?
It indicates that the price is per room, as having an extra adult in there does not affect the price.
For extra confirmation of this (although it's well hidden right at the bottom of the page) there are these couple of sentences:
All prices are per room per night unless otherwise stated. They exclude taxes and fees and are subject to availability.