Happened to discover this a while ago.
If an ad starts playing in the main window that moves the livestream to a small window in the top right corner, do the following:
- Mute the main stream.
- Hover your mouse over to the tiny window and click the PiP button.
- Unmute the PiP stream
You can now continue to watch the livestream uninterrupted. Once the ad concludes, the PiP pop-up window automatically closes and the main stream continues.
I usually enlarge the PiP window and move it over the ad to cover it.
This is basically a manual method of what add-ons like Alternate Player for Twitch.tv do.