The local Gold's Gym has a theft prevention style detector around the front door which will complain if you try and leave with a towel. The towels themselves have an obvious bump in one corner, about the size of a jellybean.
NFC is a specific kind of RFID which uses the ISO 18000-3 band for communication over short distances. There are many other types of RFID, which can have much longer ranges.
Engadget had a basic article from a few years ago. I'm not sure how the alarm works as even the distance from the floor to your suitcase might be too far for RFID:
A customer checks in and is given a towel with a customer specific RFID attached. If at the point the customer checks out and the towel is not in the room, it is assumed to be missing or stolen.
Er, no. Have you been to a hotel? They don't normally give you a single towel for your entire stay. The hotel changes the towels every day. Bulk RFID scanning during laundry lets them keep track of how many towels have gone wandering and individually track how many times specific towels have been laundered, which is probably useful information for managing towel quantities in bulk. I don't think tracking down and identifying individual towel thiefs is generally the idea, though I guess you can detect towels in places they are not meant to be (such as in their suitcases on the way out of the lobby).