It'll be interesting to see what remains after the dust settles. There are ways to separate numerology from non-biological/chemical pressured patterns. I never thought about creationists while reading the abstract. If intelligent panspermia is a thing, this would be a wonderful way to pass a communication along.
Obviously symmetry in integers is insensitive to numerical system. Where I'm struggling is in their heavy use of decimal. I can't even begin to imagine why anyone would leave codes in decimal. It's an illogical choice that we only use because of the historical accident of having 10 fingers. Anyone hiding this code wouldn't know how the system could possibly evolve. What if octopi were the really smart ones? Their numbers would still have symmetry, but wouldn't look so nice in base 8.
Yeah, looks fun! And a little dense so it will take me a few days... However, my complaints will certainly mirror those of the refutation Firebrandroaring posted. Numerology is entertaining but fruitless (except in cases when you can use it to exploit others to your own gain!)
The math is dismayingly simple. The only keys to understanding are to have a very basic conception of what they mean by nucleon numbers in the block and side chains of amino acids, and how the degenerate codons are grouped. If you can conceptualize those, you'll get it right away.