The particularist use is more accurately termed "national chauvinism", usually but not always ethnically-based, is the idea that one's own nation is in some way better than all the others, and the interests of its people should be accorded disproportionate weight.

The "in some way better than all others" bit isn't a very charitable reading of that position; if a Frenchman wants the french government to further the interests of France and Frenchmen (even at the expense of other countries), then it's a form of nationalism but doesn't include a belief that "France is better than the rest"; it's only that he cares more about France than about the rest.

Having diminishing "circles of empathy" for others depending on whether they're in your family, your city, your country, your religion or race etc. is pretty normal, but there's variance about what levels are considered as more important; (pretty much) everybody cares more about their family, but some may see religion or political affiliation or their city as a "more important" identity than one's country (this is assuming country = nation, which as you say is usually the case in the West now); "national chauvinists" would be the ones who put their country above other identities.