That sounds dangerous. It’s not uncommon for different people to order events differently, I can see two cars crossing at the same time, each driver convinced to be first.
It does lead to quite a few 'what the f.. arms up.. stares' when there is a perceived violation but it works. Probably because the cars within the stop signs are going relatively slow.
given that people generally don't spin their tires off the line from a stop sign, it's fairly safe. If it's obvious that two people are going at the same time then one that has advanced less far in that time will generally ease off the throttle and let the more advanced party continue.
there are accidents, of course, but i'm not sure of any 4 way traffic junction that's infallible.
and as others stated, right-of-way rules are observed atop the social norms.
Specification unclear. If two or more entries to the intersection have at stopped vehicle waiting to cross, a waiting vehicle is somewhere "on the right" of each waiting vehicle. If only two vehicles are present, and are across from each other, and at least one of them wants to turn across the path of the other, each vehicle is _equally_ "on the right". A relative reference is not sufficient.
Some people try clock-relative turns, but that only works if the vehicles arrived while an existing rotation (of prior vehicles) was in progress.