What he did was create a specialized compression algorithm that works very well to compress the data that is each frame of Blade Runner, and decompress it (lossily, like mp3) back into a video stream.
To put this into perspective: Blade Runner is 117 minutes long. At 25 frames per second, that is 175_500 frames.
As he says, the input data he used was 256x144 with 3 colour channels, meaning each frame was 110_592 bytes. This results in an input amount of 18_509 MB, uncompressed.
His neural network compresses each image down to 200 floats though, i.e. 800 bytes. So the whole movie as compressed by the NN is 132 MB.
A friend of mine who works with neural networks estimated his NN to be roughly 90MB at 256x144, so the storage needed for the movie he created is about 222 MB.
This means that if this technology can be made fast enough, and the reproduction high enough in fidelity, we could be looking at replacing compressors (Fraunhofer MP3, Lame, MP4, DIVX, JPEG) made to handle all types of input equally well; with compressors that can are so good for one specific set of data that compressor + data is smaller than anything the traditional compressors could create.
And even if its not fast enough, it can still be a very efficient compressor, trading size for CPU.
Plus, lastly, the NN itself can be compressed as well, and classic compressors can possibly be applied to the frame data.