How is the aromaticity in graphene different from the aromaticity in benzene? The web page Aromaticity in Graphene and other 2-D Systems begins:

I. Graphene
While the σ-bonding in graphene is assumed to be a rigid honeycomb framework built out of two-center two-electron (2c-2e) C-C σ-bonds, the π-bonding is supposed to be delocalized. However, according to the adaptive natural density partitioning (AdNDP) analysis and the electron sharing indices, graphene is aromatic, but its aromaticity is different from the aromaticity in benzene, coronene, or circumcoronene. Aromaticity in graphene is local with two π-electrons located over every hexagon ring. (emphasis added)
II. BC3 Honeycomb Epitaxial Sheet
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Update: The wording is similar to what is written in Is Graphene Aromatic? Popov, BozhenkoEmail &amp;  BoldyrevEmail (2012), Nano Research, 5, (2), pp 117–123 (open access here):

ABSTRACT
We analyze the chemical bonding in graphene using a fragmental approach, the adaptive natural density partitioning method, electron sharing indices, and nucleus-independent chemical shift indices. We prove that graphene is aromatic, but its aromaticity is different from the aromaticity in benzene, coronene, or circumcoronene. Aromaticity in graphene is local with two π-electrons delocalized over every hexagon ring. We believe that the chemical bonding picture developed for graphene will be helpful for understanding chemical bonding in defects such as point defects, single-, double-, and multiple vacancies, carbon adatoms, foreign adatoms, substitutional impurities, and new materials that are derivatives of graphene.

Question: How is the aromaticity in graphene different from the aromaticity in benzene? It is likely that those familliar with the topic will already understand the explanation in the block quote, but is it possible to find a simpler if less accurate way to explain the difference, in a similarly compassionate way to how this answer was extremely helpful to my question about double bonds and chromophores?
Simpler explanations, can by their nature be less accurate than a detailed description, but are helpful in beginning to understand things.  Getting to the heart of your question:
“How is the aromaticity in graphene different from the aromaticity in benzene? . . .  but is it possible to find a simpler if less accurate way to explain the difference,”
Perhaps a productive way to approach your question [portion given above] is to consider the molecular structure of coronene and circumcoronene while contrasting them to the interpretation of aromaticity of graphene given in your cited article.
 circumcoronene
 CORONENE
Graphene from article cited in question.
According to the computational method employed “adaptive natural density partitioning method” [we can choose to agree or not agree with their interpretation as indicated by a comment to your post by @A.K.], the aromaticity of graphene is centralized within the set of hexagonal rings.  To quote the authors “Aromaticity in graphene is local with two π-electrons delocalized over every hexagon ring.”  The salient point here being the “delocalization” is within and isolated to or restricted to [my words] a six-membered ring.
As discrete molecules, the aromaticity in coronene and circumcoronene, as depicted the PubChem structures, is delocalized throughout the entire discrete molecule and not restricted to a discrete set of hexagonally bonded carbon atoms.
In other words, it comes down to electron density distribution.  In graphene, according to the authors of the article cited, the areas of highest electrons density are within the center of the six-membered ring while in coronene and circumcoronene the electron density is more uniformly distributed over the entire molecule.
Ref:
https://pubchem.ncbi.nlm.nih.gov/compound/coronene
https://pubchem.ncbi.nlm.nih.gov/compound/Circumcoronene