I am pretty sure it's wrong. I just made a comment about this on the author's article. He claims information N~rm, but for any normal material you have mass proportional to r^3. So N~r^4, not r^2 as the author claims.
Black holes and information is a thorny issue, see e.g. [1]. So I suspect something went awry in the argument when (s)he brought quantum gravity into it.
You have a volume V1, and let d1 be the maximum density of information you can store in V1. If you try to store any more, your storage will collapse into a black hole, so d1 is the maximum density.
Now you get 8 times more data. But cannot story this data in a volume 8*V1, because if you try to use 8 volumes V1 with density d1, and place these next to each other, they will collapse into a black hole.
Thus, the more data you have, the smaller density you can use for storing it.
Black holes and information is a thorny issue, see e.g. [1]. So I suspect something went awry in the argument when (s)he brought quantum gravity into it.
[1]: https://en.wikipedia.org/wiki/Black_hole_information_paradox