If you haven't tried streaming games using either Steam's In-Home streaming or NVIDIA's GameStream feature for their Shield products, it's actually pretty awesome.
What I use it for is to play on my large TVs around the house where I don't have a computer hooked up to. I can plug in my tablet to the TV via HDMI, plug in an Xbox 360 controller through USB, and have Steam stream in its highest resolution and image quality while producing smooth gameplay. It works really well on an internal network.
Before you had to use NVIDIA's Shield products to take advantage of their GameStream feature. Now, there's a free app on the Google Play store to allow you to do that.
Limelight Game Streaming will let you take advantage of any GameStream-compatible PCs to your Android mobile device. It will send mouse, control, and keyboard commands back to your server computer and have the results streamed back to you.
The app says it will work with LTE connections, but latency can be an issue and it will use a lot of data. Your experience will always vary, of course, depending on connection factors. But in a local environment, it should be pretty smooth.
Best of all, Limelight's free so there's no additional cost.