No, you misunderstand! That's not an advertisement, it's an informational message.
no advertisement

how is that not an advertisement to be site referred to google play to get an app not developed by chess.com. if that is not an advertisement next time they can display an information that the new audi is available for purchase. All ads are also informational message.
I pay for a merchandise( a membership with promised conditions) and expect to get what I pay for. nothing less.

It's a graphical announcement. A helpful notice to let you know of a product you might otherwise not be familar with. It's an educational message to build brand reputation and foster a positive attitude towards the product. It's most definiately not an advertisement.
I pay for diamond membership and you guarantee" no advertisements" on the benefits.
on the frontpage there is an advertisement for the magnus carlsen app. I would say that is an advertisement.
please keep chess.com clean from advertisements