Fret not that your friends can cast Youtube videos from their Android device to their TV using Chromecast! You can cast anything from your Android device to your TV if you have a Raspberry Pi connected to it using the awesome Raspicast app!
Setup your Pi: You will need a Raspberry Pi with Raspbian installed on it. It is connected to your TV using a HDMI cable. You can SSH to your Pi. Optionally, you have OMXPlayer installed on your Pi and checked that you can play video files using it.
Install app: Install the Raspicast app from here.
Configure: Provide the IP address of your Pi, its port (usually 22), login (usually pi) and password.
Cast away: Play any video in Youtube app on your Android device. Click the Share option and choose Cast (Raspicast). Raspicast opens, wait for a second and you will see it playing on your TV. If you want to keep adding Youtube videos to a queue then choose Queue (Raspicast) while sharing. You can view the queue in the Raspicast app.
Use the Files section of the app to browse and play video files that are on your Pi. The UI for this is pretty basic. You are probably better off using OMX Remote for this.
Use the Cast section of the app to browse and play video files that are on your Android device itself.
Tried with: Raspicast 1.3.6