I still am not seeing what chess.com would gain from installing spyware on a chess site.
I remember, way back not long after I joined 8 years ago (back in the days of V2), the site offered a download of some kind of toolbar, or something like that (I don't remember the details). I remember researching it and discovering that it contained a well-known piece of malware. I remember screaming bloody murder about it, but it was still offered for a time after that. Thankfully, at least that episode is in the past. Of course, they never talked about that part of it, so I'll never know whether it was done on purpose or whether they were just clueless.
It's clear that the site wants the money from the ads, so it's more likely that if anything untoward is happening here, it's just sneaking in via periodic episodes of malvertising from the ad servers.
I still am not seeing what chess.com would gain from installing spyware on a chess site.