Plex Home Theater is designed as a 10-foot UI and is thus intended to be controlled via a remote control or keyboard. Plex Home Theater does not support input or control with a mouse.
If you wish to use Plex on your computer as part of your desktop experience, you can instead use Plex Media Player or the Plex Web App, which have mouse support.
Related Page: Plex Media Server > Using Plex Web App
Related Page: Plex Media Player
Related Page: Plex Apps > Plex Home Theater > Keyboard Shortcuts