Dried beetroot powder gives racing pigeons more energy, so it is supposed to be very good for them. The way the beetroot powder works is by improving the flow of oxygen within the pigeon's blood supply. This then improves the function of all of their other organs. 
Also, it is a natural supplement that enhances their energy, so it is not as if the owner is "doping" the birds to give them an unfair advantage. However, it is not listed as being an essential supplement for pigeons. Pigeons do not get all the vitamins and minerals they need from the seeds they eat. They need vitamin A, manganese and folic acid supplements, among others. All three of these are in beetroot.
Dried beetroot contains many antioxidants, too. Even if it does not provide the pigeons with more endurance and energy, it is still a good supplement for their overall health.