Throughout this thread you have a bit of an insistence on narrowly defining memory in terms of the brain, i.e. memories that people have.
In the field of epigenetics, and in computer science, and other areas, "memory" more broadly means a system of encoding information. Which is what happens here, when methyl groups physically bind to an adenine or cytosine molecule, like flipping a bit.
It's incorrect to call information stored in epigenetics "memories", but it's fine to call it "memory". I forgive the article for doing this as it's written for consumption by the broad public, and it's illustrative of the overall point if not literally correct.
FYI, the author is a respected neuroscientist: https://en.wikipedia.org/wiki/Hannah_Critchlow