Summary: One player would act as the host and would be the only one that has to own the console being used. The host would capture the video and stream it to the other guest player(s) in a fashion similar to typical game streaming, but with a program/service designed around lower latency (Twitch latency wouldn't be acceptable for gameplay). The guest player(s) would use basically any controller they can connect to their PC, and the input would be sent to the host player where it would be connected to a special adapter to the console's controller port(s).
Technical Breakdown:
1.) Host player will stream the audio/video of the console either to a streaming service or direct to the guest player(s) with whatever currently available service/application turns out to be best for real-time/low latency.
2.) Guest player(s) will use a PC compatible controller (or adapter for retro console controllers) with a custom client application that will transmit their button presses to the host player (unless there is an already existing application that does this well)
3.) The host player will run a custom host application (if an existing program doesn't exist) that will receive the button presses from the guest player(s), then transmit these to a custom adapter (probably Arduino based). The Arduino would then (hopefully) have one signal per a button that would go to a DB15 connector, then DB15 pad hacks would be made for a controller of each console to be used as the interface.
Caveats:
Latency - I'm sure this will be the main issued pointed out. While I'll agree this would not be ideal at all for professional play and/or games that need extremely fast reflexes such as fighting games, bullet hell shmups, etc. I do believe it might be viable for things such as casually playing a beat 'em up with a friend or slower games such as multiplayer turn based RPGs, video game board games (we really like Fortune Street on Wii

Using an Elgato CamLink to stream PC-Engine via OSSC to a friend over Discord, I played while only viewing the stream view for a few minutes. I could tell it wasn't as responsive as straight to my HDTV, but it was still playable to me on Dracula X. So while I doubt you'll be playing Marvel vs Capcom with your fiends online with this method, I think there's the possibility the latency could be tolerable enough for some genres. I haven't used netplay on emulators in years, but last time I did the latency wasn't spectacular on them either.
Controller Interfacing - Having to padhack a controller for every player of every console I want to use would definately get cumbersome. However I don't really know enough to make adapters to interface with the controller ports of various consoles. Basically I needed (Console controller port) ---> adapter ----> (male DB15 with Neo Geo AES style pinout). It gets even more complicated if it's a controller that has/needs analog sticks.