And no, you can’t burn them all. “Track” is also a loose term, you can do whatever motorsport you want with it... but you have to keep the transmission.
And, why “weird CVT”? Well, none of these three cars have a conventional CVT - in one way or another, they implement a CVT in weird ways, and a different way for each one.
Finally, all three of these cars were intended to be at least somewhat sporty, and all are RWD.
In increasing order of weirdness, and cylinder count:
1971 DAF 55 Marathon Coupe (at least I think this is a Marathon) - weird because it used two rubber belt CVTs (video of an older model with the same transmission design) - one for each rear wheel - and didn’t have a differential. Sure, they may be conventional CVTs, but using two of them instead of a differential isn’t conventional at all!
2002 Nissan Skyline 350GT-8 (we know it as the Infiniti G35, but the 350GT-8 specifically had a CVT that we didn’t get) - weird because it uses a toroidal CVT, rather than a belt CVT:
1957 Chevrolet Bel Air Nomad, 283 FI, Turboglide (I’d be very surprised if the pictured car actually has Turboglide though) - weird because the transmission is not actually a true CVT, but is rather three torque converters in series (also worth reading this):