There must always be a device that initiates the video stream (cast) as there is no interface or remote.
With Plex you can cast from one of the apps by selecting the Chromecast from the device menu. You can use the plex.tv web app to cast to the Chromecast.
Also note that currently you must have a Plex Pass subscription to use this feature - it will become a "free" feature in a future update sometime.