Cast, no. (That's using a Chromecast device.)
Install a VNC server on the G3 and a VNC viewer (or client - same thing) on the tablet, and the tablet can be a kind of remote G3. (VNC is normally used to gt on someone else's computer with their permission, of course] to help them with something, but it works just as well to run the remote computer and, with a fast enough connection, like your own wifi LAN, you should be able to do video. There are free VNC apps, so try it.)