The problem I see with this is that plex is just simply sending the file over the network or internet or transcoding then sending the file and the plex client on the other end simply plays the incoming file, Emulation is a whole other thing in order to be able to stream a game to another PC Bigbox would have to be running on the server computer as would the actual emulator being used, and we have no real control over the emulators so if someone was to start playing a game on a client machine then the emulator would have to be running on the server side machine and would probably be fullscreen also so you could be using the server computer when all of the sudden a emulator launches and goes full screen and you can no longer use the server side system, For this to work the way you want it to all the emulator authors would have to recode there emulators in order to send the image while still being minimised on the server side system and unfortunately I don't see this happening any time.
As for the steam link you can add any program on your system to steam as a "non steam game" Bigbox included obviously and stream to steam link or another system on the network using steam, however you will have the same issue as I described above the game or program would be running fullscreen on the server system and would be unusable for the local user.