Wikipedia states 'The GamePad's display contents are streamed as video from the console using a custom protocol and the H.264 video codec, for which the GamePad contains a hardware decoder.'
A reply to a question on quora states that a hardware decoder means 'there is a small chip on the motherboard specifically dedicated to decoding H264 video. The main A6 processor is not using or spending cycles decoding video, it has essentially outsourced that job to a highly specialized worker.'
As for software decoding, 'it's where you write and compile an application, meant to be run on a standard CPU, that will then decode the video. This is generally considered inferior, as video processing takes a lot of work, which means the CPU would take more power and time to get the same job done'
Judging by the looks of things, you might only be able to achieve this on a PC, where such software and processing power is available, and at that point, you should just use the TV as you normally do