You’re looking at one very clever piece of engineering. It’s an Adams-Farwell air-cooled, piston-driven, rotary engine. The crankshaft stays put, connected to the frame of the car, while the crankcase rotates around it to drive the vehicle. In this case, that’s a 1906 Adams-Farwell 6A Convertible Roundabout. The buggy originally came with a three-cylinder of the same design, but Mr. Farwell himself yanked that engine and plopped in the 50-horsepower five-cylinder unit you see here.
Watching it in operation is both terrifying and charming. Check it out in the video below.