New web notifications (take two)

Is there a way to stop them specifically through the settings?

Stop which ones?

You'd need to look on your browsers settings to stop those. Which browser do you use? 

I need to stop "KNVB is playing now" alerts.

But i do get important alerts through browser alerts such as "You received a new message."

This should help you turn off browser notifications: https://support.google.com/chrome/answer/3220216?co=GENIE.Platform%3DDesktop&hl=en

I think he is saying he wants to keep browser notifications, but turn off this specific one. Presumably there should be a setting within chess.com to control which browser notifications are sent? 

Yep, specific ones.

AFAIK there's now way to manage this type of notifications in https://www.chess.com/settings/notifications (yet). Maybe it will be implemented in the future.