Most PCs cannot connect 4 monitors, and 4 keyboard and mice would require several USB hubs. And of course the rendering requirements are rather high. So unless you are planning to build something custom yourself, I don't think this is an option.
If you have tablets/pcs for clients, then you can just run things as a normal client-server, like any normal multiplayer game. It scales much better to eight, too. You've yet to explain why this isn't sufficient.
I'm going to take a leap and assume that you're asking why I just don't make clients for the PCs and tablets rather than streaming to the client machines. The short answer is because I want to know if it's possible. The long answer. . . .
I remember a time when buying Diablo meant that you could install a client on a friend's computer so that you could play together over a LAN. I remember a time when Command and Conquer came with two disks so that you could install the game on another machine and play your friend over a LAN. I remember some of my best multiplayer moments happening offline, over a Local Area Network.
And then there are things like Nvidia's Project Shield that streams games from your PC so that you can play them on the couch. Gabe Newell talks a good game about home streaming being the wave of the future as well. Question: Why? Just why the hell am I streaming my games over my own wireless LAN if I'm only going to be playing single player. Sure, it'll reduce fights over who gets the TV in the living room, but if I'm running a game on my PC it's not like someone else can log in and use the computer while the game runs in the background.
Multiplayer is where consoles had PCs beat for a long, long time. If you wanted to play Gauntlet Legends, Perfect Dark, or Halo with three of your friends (or your wife and two kids) all you had to do was plug in four controllers. Yeah, split screen sucked but it was a damn sight more convenient than setting up four desktops on an ethernet hub in the same room and installing the same game on all four machines.
And yes, I'm fully aware of things like SoftXpand that let two players play the same game on the same machine at the same time. That's a work around. I really don't see there being a need for home streaming until games are built from the ground up with multiseat gaming in mind. Until I can stream the game to four players on tablets and cheap Chromebooks simultaneously, there will be no need for home streaming.
There are plenty of open source projects to test this kind of thing out with. The real problem, for me anyway, is that I don't know dick about video streaming or networked video compression. It doesn't help that there isn't much in the way of tutorials or code snippets floating around the interweb.
Executive summary: I feel that multiplayer gaming would be much easier, from the player's point of view, if they could just connect via a small web app on their device and instantly be in the game session rather than having to install the code and content resources beforehand. Also, my PC can crank out way better graphics than an Andriod, iOS, or ChromeOS device.