All of it to some extent, I think the 3rd aspect the most (enjoyment of solving puzzles).

Similar puzzle hunts are very popular in Czech Republic (https://cs.wikipedia.org/wiki/%C5%A0ifrovac%C3%AD_hra) since around 2000; traditionally, there is a path of multiple locations (~15) and several kilometers (~20) that you have to get through, and they happen over night during about 20 hours.

I am going to one in 14 days and I certainly look forward to it! I think there is other factor that drives us - breaking the routine. Similar to hackathons, these happen overnight and are designed to stress you a little as you have to focus, which I think is a nice break from your day-to-day life.

You can pick your 3 letter agency if you win

While exaggerative, I agree. Some organizations value attending and winning competitions like this one.

There is no prize as such, right?