If this is ever a thing, it will be way beyond the fifth or maybe tenth layer of information in 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.
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).