The gyroscope is recently supported in the Android Studio 3.0 emulator, released on the Canary Channel 5/17/17. Please note that (for today) Android Studio 2.3.3 is the latest official version (i.e., "Stable"). Here's how you set up a preview version for Android Studio, which may exist simultaneously with the official version. Please note that starting the emulator out of the box will not work, since this is not a completely new version: 
You need to follow the steps "change your update channel" in the last link: select File> Other settings> Default settings and update from the Channel Channel:
Please note that when starting a virtual device with Android 7+ (similar to API 26), the gyro output was shown in the virtual sensors of the emulator (in the advanced controls), it (at least for now) does not send this output to the virtual device; To see the environment in the applicationβs application, when I moved the phone, I had to use Android 7.1.1 (API 25).
(Thanks @ jamal-eason for pushing!)
PREVIOUS (6/12/17):
As of the date of writing, the release version of the Android emulator (in Android Studio 2.3.3) does not support gyro support.
While the documentation referenced by @Nesski suggests this, I offer the following as evidence:
Android SDK Virtual Reality Starting Demo is a game called Treasure Hunt. Here's what it looks like when playing on the phone . Note that the camera moves when the player is looking around.
several devices compatible with Google Daydream, because they contain an internal gyroscope - Android Studio AVD Manager offers only two of them: Pixel and Pixel XL. I downloaded two virtual devices for each of these phones so that I can run the last two versions of Android (7.1.1 and 8.0) on each device:

I ran each device in the emulator and got similar results: press CTRL + SHIFT + C (on Windows) to open the Advanced controls and you can check the phone Virtual sensors:

Using the Rotate controls, you will notice that although there is an Accelerometer output, a magnetometer output, and a Rotation output, there is no Grioscope output. You can rotate the phone as if you were looking around, but the camera view does not change when you move the phone.
While this sad reality is unsuccessful, I, however, hope and expect that Android will add Gyroscope support to the emulator in the future, as more and more developers will switch to the Google Daydream virtual reality bandwagon.