It's certainly not a luxury sports car, but in the current state of things, I'd say all sports cars are expense as they're rarely owned or operated as a primary daily drive vehicle. Owning a second car for fun certainly sounds expensive to me.
A sports car is a car intended to be used for sporting purposes, like a sporting rifle. The exact sport doesn't need to be specified, because you can use it for several different kinds of sport.
Would you claim the second an athlete leaves the field they're no longer an athlete?
"Sports" cars are tuned towards their racing counterparts. Auto racing is a sport. We don't know if that owner does autocross, probably not, but that is classified as a Sports Car regardless of anything else.