Yes, I would assume that “pak” would be an abbreviation of pakistan, or intended to mean pure.
However, what I said was, that it is not a word in British English, do you dispute this?
“Hong” is also not a word in English, even though it appears in “Hong Kong” and means fragrant in Cantonese.
It’s possible to be mislead by the presence of one store to think that some ethnic group must be concentrated close to that store. A store just opened several months ago within a half mile of my home that sells basically Pakistani food. That doesn’t mean that there are a lot of recent Pakistani immigrants (or of recent immigrants from South Asia in general) in my area. There certainly aren’t. However, there certainly are enough recent immigrants from Pakistan within a circle of thirty miles from my home to sustain a single store (and probably several stores). The Washington D.C. area has lots of recent immigrants from all over the world. The people who run this store near me probably just decided that they could open a store with Pakistani food somewhere in the general area and the potential customers would have no problems driving thirty miles to shop at their store. I suspect that the space in the local mall that they are renting is quite cheap by the standards of this area, and that’s why they chose it.
But having shopped there, I found that there are some Pakistani snacks that are quite tasty.
Sorry, I don’t think that’s a good example - PAK is simply the standard three-letter abbreviation for Pakistan, and might be used in textual form only, where space is limited (e.g. a cricket scoreboard). You wouldn’t hear anyone (to my knowledge) referring to “the Pak cricket team”.