so many ads
The primary stream is from Twitch.tv which is a separate client from Chess.com (and thus Twitch has its own ads and subscription service). Something to keep in mind: in the last couple months, Twitch released an update where ads may play automatically without control from the streamer. This was a controversial change, and your dissatisfaction is warranted.
Alternatively, you can watch their YouTube stream where ads are much less of an issue: https://www.youtube.com/user/wwwChesscom.