Because they would clearly have to...? The Qunari population is now many times greater, and they have a vested interest in classifying everyone quickly and optimizing the roles everyone is assigned. They now need a word for their race, because "Qunari" just means everyone, now, and those individuals who are large, gray-skinned, and horned are the only group that can't be easily and quickly described with a single word that gets across everything we need to know about them as a group, physically.
There are other titles as well as Qunari, there is your role, there is Viddathari who are new converts (usually the other races are called that) and they probably refer to humas, elves and dwarves as exactly that if they need to. You seem to be saying they need it for their paperwork but I don't think that they do. If someone is of another race and that needs to be clarified then I would assume they do that and maybe if it isn't it means they are qunari Qunari? Now I have no idea if this is the case but it solves the problem does it not?
As for descriptions, I don't know if many descriptions within a Qunari society would need race references as they would be more likely to describe someone as their role anyway.
Yes, but they seem to focus on it, exclusively. We have yet to see them group people based on anything other than "not belonging to the Qun" or their race, even though the latter is apparently not important to them.
you seem massively hung up on this "not important" thing, I really don't think it is as important as you seem to think it is.
They exist to make conquering easier in the future. And the Arishok dropped that attitude because Hawke demonstrated that he/she did understand, and because the Arishok was in the middle of conquering a city.
and to do that they would have to.............. pander to the worldview of others, or at least appear to. That was my point. How is that not the same thing i just said but phrased differently? Yes the Arishok dropped the attitude because he realised Hawke already knew about it and it was no longer beneficial to keep it secret. Not because he thought it was too complicated for non Qunari to understand. Isabela stole a book, that book was important to the Qunari (for religious reasons), they weren't leaving without it. Not hard to grasp at all but probably better to keep a secret seeing as the tevinter Imperium really wanted that book.
Because they're dealing with spies, of various races, loyal to the Qun. They would need words to distinguish that this spy is an elf, and this one a human, and in Iron Bull's case, that this one is big, gray, and has horns.
elf, human, dwarf, Qunari, Vashoth or Tal-Vashoth or Qunari, Qunari, Qunari, Qunari. There are lots of ways to differentiate.
I'm pretty sure David Gaider has indicated otherwise.
Hmm, where?
"user@BioMaryKirby Is there a good way to to refer to said race that doesn't imply their religion/philosophy or rejection thereof? Am curious 
Nope! The Qunari don't need one, and the rest of Thedas sees all giants as the same. The only people who care are Tal-vashoth."
As I said, there is no name for the race specifically and it is wrong to say it is Qunari but you can call them Qunari because they are Qunari.
Yes, but I'm saying that they would probably use race to distinguish strangers among the Qun, in much the same way we do in real life. It's a description of someone. So when someone nearby says "...oh, the new Arvaraad(or whatever)...etc..." and they need to clarify, saying "the short qunari" wouldn't really be clarification, because that could mean an elf or a dwarf or a qunari who just happens to be only human-sized. And while, in that example, many would not be confused, there are also many people who would.
I doubt they describe people that way at all but maybe. They don't live as the rest of thedas does, they don't have the same social lives or connections. The distinction probably matters to the Tamassrans but probably not to anyone else, at least not much.