I think because chess is so very difficult, so challenging, so impossible to master, some people have the urge to elevate it to the level of sport. Because sports are ALSO very difficult and challenging.
But what makes sports so difficult is the physical skill component. It's the ability to train the muscles and/or have the natural ability to move those muscles in a specific way to get the desired result. Chess is not like that at all. Chess is a mental pursuit, not a physical one. Sports are mentally demanding too, but on top of that require the physical skill component. Chess is almost the anti sport, where little to NO physical skill is required.
"As society has evolved, many now view sports as having a broader definition, but it is important to acknowledge that many others still believe that physical exertion and athleticism are essential components of what defines a sport. This view emphasizes the health benefits and the unique challenges associated with physical competition. And many organizations like the Council of Europe define sports as forms of physical activity aimed at improving fitness, well-being, social relationships, or achieving competitive results. This highlights the continued importance of the physical aspect in any formal definition of 'sport'."
-Wikipedia