There is not a lot to say/add about the beauty of riding a fixed gear.
It is only by trying such bicycle that you will understand what is great about it.
Riding a fixed gear bicycle gives a unique feeling of being part of the entire machine.
…a very rudimentary machine, but moves with the person as you are riding it… Source
Here is a short video showing a few riders enjoying the ride (not a race) and a bit of skidding.