This is pure nonsense. Random data is provably not compressible. So all the complex schemes the author came up with are useless, and it's not just due to a lack of CPU power that it failed to show results.
I was teaching myself programming using QBasic and I had just discovered the random number function. My idea was essentially to find a random seed which would make the random number generator generate the same byte sequence as the input block. Then you just had to store the random seed, huge win!
Of course, it didn't take me too long until I realized just how long it would take to compress, and I hadn't even thought about the limited number of byte sequences a 16-bit random seed could generate or the fact that the random numbers it would generate aren't all that random...
But for a few hours there I felt really, really clever :)
A more specific objection is that the ‘pigeonhole principle‘ applies.
Another way of looking at it is reducing it to absurdity: if it worked, you could repeatedly apply such a compression scheme until you are left with just a single bit representing the original data.