Kainy is a remote desktop application that is free/purchase application found on google play and ouya stores. It is primarily used to play games with, but you can use it for simple taskes aswell such as watching and listening to movies and music. Purchasing it off course unlocks more features and functionalities to the program, which I will be covering the purchased version.
Unforchantly because it is network based you have the limitations of networking weather it be lan or over the internet, unlike with nvidia shield which is lan only. The application does not depend on what brand of hardware you have unlike the nvidia shield does, so nvidia fanboys cry me a river streaming pc games to android devices isn't exclusive to nvidia devices and hardware. As much as you try to shove that down everyones throats we can practically do the same exact thing with kainy and any android device with any x86 PC with windows.
The one major down side to kainy is its windows and android only, so no iphones, osX, linux, or bsd capabilities. With SteamOS being a linux distribution it will not work with that, unless they add linux support down the road for kainy. Don't worry too much because there are other remote desktop applications that can handle gaming on these platforms just fine.
Other than that you have many many options client and server side, you can allow others to view what you are doing with extra slots, you can limit the information sent and received client & sever side. If you are worried about security in order for someone to control your computer they need your IP, password, and kainy ID. My password is 19 characters long with letters, numbers, and its split into sections with special characters. The Kainy ID is split up into sections and varies in length. So it is much more secure than most remote desktop applications I have used that go over the Internet.
You can also customize your controls live on ouya, on smart phones and tablets you have to setup a control layout which can force you to leave the server you are connected to and reconnect after you have it set up. You can also just use kainy as a way to make your smart phone or tablet as a controller for your pc. For ouya if you do not have a bluetooth dongle it is another way you can use the ouya controller as a controller for your pc, if you have bluetooth capability and you just want to hook up your ouya controller to your pc click here for a tutorial.