In my physics courses we would routinely talk about 6 dimensional spaces when discussing position-momentum space, also we would sometimes refer to two dimensional objects like a moebius strips as "1-dimensional".
> also, if we're using that definition, does that mean I have a 7D SSD?
Maybe. You can use whatever definitions you want if you feel it's helpful. However, based on your description, if you're using a single bit as a dimension, you should figure out how many bits the the dimensional information encodes. As it stands, it's not clear what you're counting as a 'dimension' in this context. Also, normally we think of degrees of freedom as being independent of each other (hence the claim to 5d in this example). The charge information would normally be thought of as a single degree of freedom, so you'd have a 4d nand disk.
One reason it is helpful to think of "a dimension" as an independent degree of freedom, is that it becomes a parameter you can focus on improving. So if you say "Well what can we change, or make more precise?", the answer for the nand case is "Well, we can't easily add another spatial degree of freedom, but we can improve our stacking to improve how much we can pack into the vertical dimesion (but we're limited by Job's obsession with thinness). We can improve our measurements of spatial resolution, which will affect 3 of our dimensions, but not the charge. We can also improve our charge resolution. Let's figure out which one is cheapest to scale."
Now granted, sometimes tweaking one parameter affects the other, so they aren't strictly independent. You can pack a lot of charge on a NAND, but as the other dimensions get smaller, you start having increased difficulty with leaking.
Anyhow, I think there's more here than you're giving them credit for, even if they are guilty of tooting their own horn a bit (shocking).
But yes, the article presented here would be greatly improved if it gave examples of how to classify existing technology using the researcher's dimensional classification scheme. It's a common scientific writing tactic that I'm surprised was not used here.