HP requirements to drive the supercharger are typically quoted in the 800 HP to 1000 HP range. This is with the driving crankshaft being around 8000 - 9000 RPM.
If it was just a question of handling 800 to 100 HP, the drive (while large), wouldn't be that difficult to design to work properly. However, the system has a lot of unique load situations that really stress the belt. The torque fluctuations from the engine resemble barely controlled explosions. The speeds are high. The heavy loads make it likely that shafts will flex and belts will track to the outside flange edge. During tire spin conditions, drivers have to "pedal" the car. This is a method of getting off and back on the throttle very rapidly in an attempt to get the tires hooked up and stop the tire spin. When this happens, the driving RPM drops nearly instantly from 8000+ RPM to a couple of thousand RPM. The inertia of the supercharger takes over at that point and it tries to become the driving shaft. This creates havoc in the belt, as the tight and slack side spans in the system are reversed, creating high shock and compressive loads in the tensile cord. Add in the virtually instantaneous load application when the cars leave the starting line, and you have a very difficult, very damaging application.
An 11mm pitch Poly Chain GT belt was specifically designed for this application. The 11mm pitch gives more speed ratio flexibility than the previous 14mm pitch belts, and 11mm belts have more strength and ratchet resistance than 8mm pitch belts. A specially designed tensile cord is also used to handle the loading situations described above.
Add all that together, and you have the situation you'll see on any typical weekend NHRA race. Top Fuel and Funny Cars going down the track, round after round, reliably. Its one of the 7 belt wonders of the world.