Gzip on genes is something I wondered about for a good while (since I read about "language trees and zipping" about 20 years ago[1].) Pleased to hear someone tried it!

I was wondering in particular whether anyone looked at "junk" DNA with gzip, etc., as a test of how randomised it was.. Do you know if that ever happened?

1: https://arxiv.org/abs/cond-mat/0108530