It sounds like they struck a deal with chess.com to put a bookmark that opens a regular web page. It's no more "baked in" than accessing the same website via Chrome or Safari.
By the way, check out lichess.org. Free, open source, no ads, interesting architecture, servers that don't crash, feature parity with chess.com.
I've seen it with a few popular content creators getting their own "custom version" of Opera where it has an on-brand theme and links to their content directly baked into the browser download. Presumably there is some kind of customisation pass that thinly wraps the regular installation process.
I don't personally get the appeal but maybe big brands are more likely to feature the browser if it's customised (eg. live streaming a big chess.com game where the "official" tournament client is the Chess.com Opera Browser).
Well yeah, it says that right in the first sentence ("exciting new partnership..."). It'd be unlawful if they didn't prominently disclose that this is a paid endorsement.
There's a diversity of both paid and free chess servers, and the paid ones don't hold any particular advantage today. This kind of ad (it *is* an ad) takes predatory advantage of people unaware of the internet chess landscape, to funnel them into handing over their wallet when it's completely unwarranted. (See e.g., lichess.org [0]).
And all this Opera stuff is baffling to me. Why would anyone choose to put advertisements in their browser, in any form? Ads don't inform you–as this example shows, they mislead and prey on you. The conventional defense of ads is they fill in information gaps: they tell you about services you want but didn't know were available, like an interesting restaurant on a nearby side street you've never visited. But it's so much more often the opposite: this ad convinces people to pay for a service they don't want and don't need. It takes advantage of information asymmetry, of the consumer's lack of familiarity with the product domain: it doesn't flatten that asymmetry, but exploits it.
It takes authentic humans, like me right here, to tell you "internet chess is free and you probably don't want to pay for it like all the ads tell you to". No commercial agent will do that.
Sponsoring players and influencers certainly helps cementing their brand.
That contradicts what I have been hearing. And it makes total sense. Unlike on lichess, the incentives are wrong for chess.com to remove whale cheaters.
Special guest - Vladimir Kramnik, who has being researching cheating in chess with stats, quite intersting / disturbing