If you only have 8 samples per row, then you have 7 adjacent pairs. If you use a bit to represent the differences, you'll only have 7 bits. If you want 8 bits, you need 8 differences, so 9 samples.

That makes sense, but why does the example have a 9 by 9 grid, would it be a 9 columns but only 8 rows?

Yes, you are right, it's a mistake in the text. I'll correct it.