I don't know of any video capture solutions for android devices, and I figured injecting any additional hardware like another PC was not feasable.
By leveraging open and known standards, iOS and Android can both be used. And considering the OP is coming from a device that has no outside connectivity aside from a USB 2.0 port, I figured it would be understood by him that additional hardware is needed in some form or another (an all-in-one appliance or utilizing a PC).
I would personally use RTSP to stream by taking a high def video source, compress it on-the-fly into h.264, encapsulate it with some sort of RDT (I like the open-source Open Broadcaster Software), then stream it over the network. All you need is a video client that can read pick up RTSP streams plus the underlying video container and you're good to go. VLC has done this forever, but there are many other apps on both platforms that will do it too.
You could do the above with an HDMI capable capture card on a computer for around $200 like the BlackMagic Express, with on-the-fly compression (easy if you have a CPU supporting quicksync); or spend huge amounts on an all-in-one appliance for the broadcast field, like the Cube 255 that creates a stream and transports automatically over Ethernet, or 2.4/5Ghz Wifi (for the low low price of ~$1,200).
Either way would be close to real time, but still more than likely not real time enough for video gaming (at least 2 second delay more than likely).