Humor has nothing to do with the incorrect definition of the number of dimensions of an object.
Which is why I mentioned your pedantry.
Let me draw you a diagram _________________
That is a two dimensional non-solid object since is has a height, one pixel, and a width, more than one pixel.
In fact, since it's drawn with electrons, it's got depth too. Actually, since it's drawn as pixels on your screen, which by now are probably discrete LED components, it's much more than that.
It's a signal which causes a series of diodes to emit a color which your eyes perceive as a straight black line -- in reality, it's none of those things either.
Look, you can be as pedantic, reductionist, and anal retentive about this as you like
For purpose of explaining this and discussing it, they defined a plane in terms of this sheet of atoms with this particular layout.
That's it. There's no mathematical chicanery going on, and everybody knows it's not, strictly speaking, either a plane or a 2D structure. But it's got some characteristics of a plane, and, for purposes of discussion, is being treated as a 2D structure.
Because, if they had to say this 3-atom thick sheet of interlocking atoms which demonstrates some characteristics of planarity, and allow us to connect them together while maintaining the same type of planarity it would get awfully tedious.
In reality, it's probably not much different than LEGO.
Seriously, get over it. It's almost impossible to discuss this kind of thing without it turning into a tongue twister unless you come up with some form of metaphor.
The rest of this
Yes, excellent, from a mathematical perspective it's not 2D. But, for purposes of discussion of these material properties, they're calling it a plane.