If they're trying to dissuade "universal compressors" then Mike needed to ask for the algorithm first, and then generate his file. If you tell me "I bet you can't compress this file!" then I can do whatever I want to write some stupid one-off compressor to shave a byte off and take your money.
It's a limited risk. Even if the file is compressible by one byte, it's very unlikely you can figure out how to get a decompressor functioning without plenty of bytes of overhead. And even if that problem disappears, he'd still win 99.6% of the time.
And you can get rid of that risk by requiring 100 bytes of shrink. Just measure the size right.
As someone else said, if the reward was a million dollars then this becomes a game theory problem.
If you have $100 in disposable income it might be worth the lark if the officiant is uncareful with their chosen text. Though odds are good he pulled it from random.org. That’s where we used to send people.
I think it would be better to require a meaningful percentage (say 1%) of compression rather than an exact count of bytes. Especially while people can ask for arbitrarily large files.
The chance that a randomly generated 1KB file can shrink by 100 bytes is the same as the chance that a randomly generated 100MB file can shrink by 100 bytes.
And that chance is too low to distinguish from zero before the universe dies.
I'm not saying 'Mike' had a high-effort ask, because clearly it wasn't particularly well thought out. Just that other people were glad for any Mike at all.