Nielsen identifies a quantity, a ratio of "Casimirs", which he thinks is maximized by the particular gauge symmetry groups and space-time symmetry groups that we see.
He has previously had the idea that some of the observed properties of physics are "random" or "accidental" - e.g. that there is some complicated deeper theory and the simple observed symmetries are emergent from it with high probability. On page 6 of this paper, he gives his intuitive justification for why his special quantity might be indicative of such an origin.
He wants to identify the groups that are "easiest to become good symmetries by accident", and (if I'm reading his prose correctly) the indication of this is to be that the matrix representation of a group element does not change much, as the group element is varied. (He proposes specific measures to quantify the amount of variation in the group element and its matrix representation.)
Although this is his motivation, he also adds that there might be some other reason why this ratio of Casimirs is maximized.
As for this work's reception... the calculation is not very strong evidence of anything (the symmetries and dimensions of observed physics are small and could be singled out by many other simple properties), and there isn't much idea of how the deeper theory works or how the emergence works. So it will get attention from people already interested in his "random dynamics" research program, and maybe from a few people working on "landscape" or "multiverse" theories.
