When the original Apple Watch was released back in April 2015, one of the features that appeared to get lots of attention at the time was the ability for the Watch to unlock doors (https://9to5mac.com/2015/04/24/apple-watch-hotel-room-key/ is a good example of this). From a technical point-of-view, how is the Watch able to unlock doors in this way - is it purely based on the NFC chip inside the Watch, or does it rely on a companion iOS app running in the background on the paired iPhone?
The example you reference is actually not implemented using NFC at all.
Instead the lock in the door is Bluetooth-enabled, and the app on the Apple Watch thus uses Bluetooth to communicate with the lock for unlocking. Today the SPG branded app has changed into a Marriot-Bonvoy branded app, but still works on the same principle. If you look at the FAQ for the app, you'll notice that it instructs the user to ensure that Bluetooth is On.
The process does seem to rely on a companion app on the iPhone for initial setup at least. From screenshots it seems the Apple Watch app can show the error message "Phone unreachable" during unlocking, which seem to indicate that the phone needs to be present.
To put it simply, the Apple watch acts like a key fob.
You've probably seen these credit card "keys" or these fobs on a key ring that people put up to a sensor on or next to a door to grant them access. (HID is the dominant market player - I just grabbed a couple of images from their site).
These devices just a have a very simple RFID transmitter in them that sends out a code, usually Wiegand, when put close enough to a reader. The reader communicates back to a server with the code that was presented and send either a "yes" or "no" back to the reader which then operates a door lock. This is basic access control.. Below is a (very) simple block diagram of how a typical system is laid out.
The controller (blue box) handles the reading of the cards from the sensor (gold circles) and the (un)locking of the doors. In fact, the controller has a large bit of memory stored so that permissions can be pushed to each door and the system will continue to function even if the server is down.
The Apple watch (and iPhone) has the ability to "read and write tags" with their NFC chip. So, the NFC chip emulates a card or keyfob by transmitting the ID code. The door reader still communicates back to a server to get authorization to grant/deny access. So, just like the key fobs/cards don't need any special software or apps to function, neither does the Apple iPhone/Watch.