How to stream only the video to an Apple TV from a Mac?
There are two ways to send content via AirPlay from your Mac to your Apple TV when it comes out of the box. The first is the Mirroring method, found, as you mentioned, in the Menu Bar on OS X and in the Control Centre on iOS. As far as the in-app method goes, the only app that supports that is iTunes. There should be an AirPlay icon at the top of the window to send music and movies to your TV.

There is some third-party software available for sending content via AirPlay, as well. First of all, I have not personally tried these methods, so keep that in mind. The first is Beamer ($15), which can take video files and send them over to the TV. The second is AirParrot ($15), which allows you to mirror content as usual, but it also allows you to have the TV act as a second monitor or to beam over a single app (so you can send any single app over, like QuickTime or a web browser).

Then there is the tried-and-trusted option of just taking a video cable and connecting your Mac that way. I don't know what Mac you're using (might not be so feasible with a desktop) but AirPlay has in my experience always had some latency and picture quality drop associated with it (same goes with the Chromecast and other wireless display technologies I've tried in the past) and just using an HDMI cable should give you a speedy, high-quality output. It's the option I'd choose most of the time.