Errm, to be honest I've never been interested in these kinds of techs, but when people talking about Shield enabling you to stream to a tv, plenty of people said there were other devices you could do this with. No idea if they were Nvidia only, AMD, or other.
Eyefinity is not what you are looking for.
Are you talking about streaming in your house to a tv, or talking about outside the home.
Gamestream or whatever it's called has two modes, one is streaming in house via PC, the other is streaming over the net via Nvidia's cloud. As with other cloud solutions it's laggy so presume it's as problem infested as all other solutions. Either way AMD has their own cloud thing coming, here, I honestly have no idea about it. They've mentioned cloud gaming and my brain shuts off to save itself from the stupidity of gaming with insane lag.
Steam is trying to do it's steamOS/steambox thing, build a box, sit it next to tv, and it can stream games from Steam on your main PC... seems a bit daft. It will also play games in SteamOS directly without the main PC< but only ones that support SteamOS currently which is essentially a few first party titles as yet. A cheapo APU, mini itx box with SteamOS streaming from PC might be fairly decent in the near future.