The mini-cars that the Shriners drive in parades are a type of go-kart. As of March 2015 they are supplied by Promo Karts USA of Onarga, Illinois.
While Promo Karts currently makes the specific models that the Shriners use, similar custom go-karts can be made by a number of similar automotive companies.
Go-karts typically have a small 2-stroke, 4-stroke or electric engine. They can be licensed for use on public roads in some countries but may need to meet certain safety requirements. In the United States, go-karts are generally not allowed on public roads but can be driven in designated public areas for off-road vehicles.