I think it has a lot more to do with popular chess streamers like Hikaru, Botez sister, gothamchess etc. Andrew Tate promoted a lot of stuff and but I never came across his chess content and I follow chess content quite a bit. Also, I just googled what his chess rating was and his dad Emory Tate [1] came up, so it seems like he isn't even the most influential chess player in his family.

[1] https://en.wikipedia.org/wiki/Emory_Tate