That’s a beautiful bike. Have fun with it!
I’m planning on racing a tri using a fixie next year, just for the fred factor.
As to why would one want or need a fixie… it’s a pure biking experience. Every ride is a new adventure, hills that are fairly easy on a regular bike can be really hard on a fixie going up, but they can be even harder going down. You go as fast as your legs spin.
The bikes themselves are as simple as a bike can get. Nothing to break (well,all the parts can break, but no complicated parts).
Some claim (a lot of people) that riding a fixie teaches proper cycling technique, but I’m too new to riding fixed gear and single speeds to be able to comment.