There's a list: https://en.wikipedia.org/wiki/List_of_organizations_with_.in...

I don't see why a non-western military alliance wouldn't be eligible, so long as the meet the criteria — treaty registered with the UN etc.

Even if they dejure meet the requirements, I suspect that IANA would be under heavy political pressure to deny the claim.

I suspect that exactly no-one cares about .int domains

They would, but even orgs that have historically had .int domains tend to move off them to either their own TLD (like CERN moving to .cern) or to other gTLDs (like the Commonwealth of Nations from commonwealth.int to commonwealth.org.) Ironically, NATO was using .nato briefly in 1990 before moving to .nato.int

So, CSTO using csto.org rather than csto.int is probably just keeping up with the times, not failing to get an .int