Wikipedia article linked also says "As of 2018 the concept is loose and evolving" linking to a newer article than the UN report, so why would I think this paper used the UN definition?
The Wikipedia article further goes on to state "The utility of the NOVA classification has been subject to criticism. However, a 2018 publication from the founders of the NOVA classification uncovered misleading and incorrect statements in the critical appraisal, as well as non-disclosed conflicts of interest."
Basically, I don't see a terribly agreed upon definition. Things point several ways, and the GP's concern about definition is entirely valid.
> so why would I think this paper used the UN definition?
Because if you read the paper from the OP link, the authors cite that their definition of ultra-processed food is from Monteiro et al 2008 viz. the same UN definition the OP refers to which is widely agreed upon.