Wow, those two columns seem pretty pointless, seeing as they are completely the same everywhere except when they’re blank. It seems like it must be referring to the fact that it’s the 2nd, 3rd, 6th and 7th scale degrees that provide the different colors of the modes, while the 1st, 4th and 5th are more stable, foundational tones.
For example, the major and minor modes of classical common-practice music are the same when it comes to their 1st, 4th and 5th (and second!) scale degrees, leaving only the 3rd, 6th and seventh to determine their distinctive colors.
However, it’s not clear to me why the tonal tones for Lydian don’t still have 1 and 5, or why there aren’t a 1 and 4 listed as tonal tones for Locrian. Further, it seems a little iffy to refer to 2 as a tonal tone equal in significance to 3 and 6, when it’s only implicated in the Phrygian and Locrian cases. Further, it seems pointless to have both tonal and modal tones be completely blank in Lydian and Locrian just because of their unusual 4th and 5th degrees respectively.