I did find one canon reference. FM: Mercenaries Supplemental II, page 18, talks about Noisel and the games. There's a sub-section written by a spectator/participant of the games.
Quote: "But if the shock of seeing one Atlas decorating another for dressing up like Saint Nick wasn’t enough, the show really got started the next day, when the first of the “talent competitions” began. Ever see BattleMechs relay race through a river valley? Or how
about a game of BattleMech football—old American rules, by the look of it? If not, you’re missing out, and let me just say right now
that a Gauss rifle is one hell of a way to sack the quarterback, and five flights of LRMs makes for a hell of a blitz!"
So there's at least a 'mech relay race on Noisel. Which makes sense to me.
I don't think there would be 1 answer either though. More likely several different events with different rules around them. Some would be shorter and perhaps in a track or track-like setting. For a LOT of participants, I think something akin to a cross-country race would be more likely, with tough terrain being a big part of the challenge.
Also don't just think of racing cars as your baseline of comparison. That is valid. But also think about human foot races in the real world. And think about how some of that could be adapted to a 'mech race format. The concept of a relay race being an excellent example.
In real life, think about the array of racing (cars and people/foot) that are out there. The array of different types of races with different rules. I imagine the big Battletech universe would be similar. It is a big universe. What participants are doing on Noisel may look very different from some illegal industrialmech racing like something out of the first Fast and the Furious movie happening on some other world.
As for equipment like MASC or Superchargers. There are real life racing where practically anything goes. If you can afford to buy it, you can use it. And there are other racing structures where things are extremely restricted to level the playing field. I can see both happening. Even within the same set of events, you could have one race where anything goes 'tech wise, and another event by a different name where things are much more restricted. Each entertaining in their own way.
Sounds like Noisel gets to use weapons. Other places may be much more severely restricted and not allow it. Just like how combatants on Solaris and a few other 'mech fight arenas around the Inner Sphere and yet in most other places I'd imagine 'mech use to rely on simulated weapons use.
So no binary answers here. This is definitely an area that seems to exist, yet we know little about it from canon sources. Leaving a lot to your imagination.