I'm almost entirely ignorant on this topic but it sounds like you're suggesting this could be a thing, which is more than the other posters here are currently saying (although it's early days yet, with only a handful of comments).
The things you've just mentioned sound like properties of the sequences, whereas the site sounds like it's describing something which modifies the meaning of the sequences depending on how they're physically located. Ie if gtta is resting next to tacg or whatever it'll have a different meaning to if it was next to gata.
WildUtah is referring to chemical modifications (methylation, associated with epigenetics: http://www.whatisepigenetics.com/dna-methylation/), the structure of [eukaryotic] genes (intron/exon, start and stop; things many elementary students know of -- and subsequently forget) and palindromic elements.
Palindromic elements are most closely related to what the linked paper is about. Basically, instead of existing as a normal double helix, the two strands separate and bind with the palindrome on the same strand; like making an X with DNA: https://en.wikipedia.org/wiki/Palindromic_sequence .
Ultimately, this is a crappy press release for a paper that, as _of points out, is scientifically correct but otherwise dull. The paper is going back to first principles, as it were, for DNA and looking at factors in DNA alone that contribute to its function (well, 'normal', non-methylated, potentially histone associated DNA).
The things you've just mentioned sound like properties of the sequences, whereas the site sounds like it's describing something which modifies the meaning of the sequences depending on how they're physically located. Ie if gtta is resting next to tacg or whatever it'll have a different meaning to if it was next to gata.