It should be in the bottom left corner once you click the YouTube TV button at the top of the menu. I recorded a video showing how to use it. https://i.imgur.com/CwvpAAO.mp4
Is the cog button not there for you? They might be testing a new interface for some users. Please edit the review and let me know if the interface looks different for you, so I can look into this more. Thank you

What do you mean by "You need youtube TV?". That's just the version of YouTube that usually runs as an app on TV's. It's not a paid service or anything like that. A key feature of YouTube TV is that it let's you cast, while the normal browser version doesn't. This extensions lets you access YouTube TV in your browser as well, which is not available otherwise.

Thank you for leaving feedback. It's unfortunate to hear that it didn't work for you. When you click on the extension icon in the browser, there are a couple of steps to follow, in order to start casting. Can you let me know which step was causing problems? I'd like find the root of the problem, so I can fix the extension.