It looks like they're using the NOVA classifications[0]; there have been a couple of other articles relating to the same system posted here recently, e.g. [1].
The NutriSource in "Whole milk (Cloverland) with NutriSource fiber" is apparently 100% partially hydrolyzed guar gum[2], which I believe would qualify the combination as ultraprocessed under this part of the definition from [0]: "Substances only found in ultra-processed products include some directly extracted from foods, such as casein, lactose, whey, and gluten, and some derived from further processing of food constituents, such as hydrogenated or interesterified oils, hydrolysed proteins, soy protein isolate, maltodextrin, invert sugar and high fructose corn syrup.". By contrast, skim milk (as used in the unprocessed menu) has nothing added, only removed, and so would fall under their Group 1 "unprocessed or minimally processed foods".
As for whether this is actually a useful classification system, I don't know. I have no reason to believe any of the studies are bogus, but taken as a whole, it does seem like an attempt to launder the naturalistic fallacy into some scientific respectability.
[0] http://archive.wphna.org/wp-content/uploads/2016/01/WN-2016-...
[1] https://news.ycombinator.com/item?id=19930970
[2] https://www.nestlehealthscience.us/brands/nutrisource/nutris...