That's a long question, can you do it step by step? yo!
why do people use 'international'?

Maybe "international" refers more to their preference than to their location.
(Let that comment roll around in your noggin for a while as you try to figure out what I mean.)

Hey C-captain:
tell me about this new spiritual energy infusion...and is there really an uptick in natural disasters? I am not well-read on that part. But the rest of it is an interesting idea. At what point does the global economy (international trade), the global network (proliferation of shared knowledge and interaction), etc., become a global culture? It wasn't that long ago that borders meant a strong compartmentalization of peoples - what's the (pardon me here) endgame? In my opinion the endgame is never one people. We're hardwired to form groups; however, the groups are constantly in flux.
In very-slightly-big-stretch-kind-of-ways I'm reminded of a phenomenal book I just read called Anathem by Neal Stephenson. Okay it was the audiobook - but truly amazing writing and ideas.
But as to your original question, I have no idea :) Maybe they're not ashamed/unpatriotic/etc. but rather don't want to be judged based upon anything other than their chess or their chat-based personalities. Anonymity.

Maybe it's because some guys live in corrupt miserable countries with poor human rights (and even worse sanitary conditions!) so the international tag is a convenient way to blend seamlessly in with the rest of humanity.

I suppose for many people. it could be a statement that "my nationality is not important to me". After all, it's the only stat that's contained within the person's post. There's no age, gender, race-because we feel that doesn't really define a person on-line anymore. For me, my nationality has probably defined me and I do identify as Czech, but I fully understand a person who considers nationality to be irrelevant.
On this site, do people put 'international' as their place of origin or where they live because they loathe nationalism, or because they feel that they are citizens of the earth and the time for borders, while not past, is perhaps more unimportant than in the past due to humanity's worldwide ability to communicate and share instantaneously along with the subsequent quickening and concurrent unstoppable careening of our world/consciousness into the fifth dimension as evidenced by the uptick in natural and man made disasters,the financial and religious meltdowns, and the new infusion of spiritual energy into the planet, or what?