I doubt anyone would argue that (say) a famous game (chess or not) champion is comparable to a great mathematician in mental accomplishment or mental ability.
That’s where we differ: there is no doubt in my mind that mental ability of chess genius and mathematical genius correlate. Playing chess at higher levels requires the same set of abilities required to be able to learn and exercise mathematics. Deep memory, flawless knowledge and application of formal logic, ability to critically examine ‘a problem’, or, for chess, ‘a position’.
As for “comparable” - lets see if any chess players proved, over centuries, that their genius is in fact comparable to genius level intellect required by mathematics:
Mikhail Botvinnik - The father of Soviet chess, 3 times world champion, PhD in electrical engineering, developed first Russian chess computer, AI researcher.
Max Euewe - 1935 world chess champion, PhD in Mathematics, wrote several books on chess and math.
Kenneth Rogoff - chess GM, awarded in 1970’s. Also served as chief economist at IMF through 2001-03.
Jonathan Mestel - GM, 3 times British chess champion, professor of applied maths, Imperial College London.
Emmanuel Lasker - held the title of world chess champion for 27 years, PhD in mathematics, algebraic geometry researcher, Lasker-Noether theorem named, partly, after him.
There are many more.
It’s fairly obvious to me that chess champions and aristocracy, if I may call them that, are the people suitable for the highest posts in academia, science, engineering and many other fields. Equally, many great scientists have the mental ability and depth to train themselves to perform at the highest levels of chess. That is because chess ability and science prowess are both abstractions that stem from superior intellect. There is no such thing as chess intellect, which applies only to chess and nothing else. There’s just Intellect, which can be applied to and learn from many fields, including chess and mathematics.