Oxford Languages defines "sport" as "an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment".
By that definition, anything that doesn't involve physical exertion is not a sport. In loose terms, it's a sport as much as, say, chess is. No physical exertion, but the element of competition remains, so it all depends on how strictly you define "sport".
I have a response to that claim, but I didn't write it, its from:
https://beyondtheflag.com/2017/10/21/racing-three-reasons-its-a-sport/2/
The definition of the word “sport” states that sports required skill or physical exertion. Racing has both, so there is no doubt about the fact that it is a sport.
Some people believe that racing isn’t a sport because “anyone can drive a car”, thus meaning it doesn’t really take much skill to do it on a competitive level, which would make it not a sport. However, this is simply not the case; driving a race car going four times as fast as you would on the highway and doing it against dozens of other drivers is not something that just anyone can step up and do.
The skill involved in driving the car itself is excessive, as is the skill to be able to manage everything else that’s going on around the car, both inside and outside the cockpit. Gearing, fuel and tire management, pit strategy, competitors and the strategies of competitors are all things that drivers need to keep in mind during ever lap of every race. That takes serious skill to be proficient at.
As far as physical prowess goes, it takes hard work to be able to handle a race car, especially for the time periods that drivers do. Take a look at this video showing how many G-forces IndyCar drivers experience during races.
In addition to dealing with G-forces much larger than athletes in the MLB, NBA, NFL or NHL, drivers can also lose anywhere between
5 to 10 pounds of sweat in a single race…sometimes more. It’s pretty obvious that race car drivers have loads of physical prowess and need it in order to race, so racing is clearly a sport.