Hi! I completed a run "Obtain Item : Netherite RSG" and when I started the run, I had to run through a village to find some cave, but I haven't been using any resources the village had, so does it count as a "Structure" run or a "No Structure"?

It still counts as a structure run. If you want to do a no structure run. you have to turn off generate structures during the world creation.

nah, from my experience that rule is much more complex and controversial, they have rejected many of my runs just by having a village which i didnt use or a mineshaft, but they have accepted many other rsg wr runs with structures, ej: greenflee´s enter nether rsg ns wr, Mathox first sub 2 enter nether rsg ns wr, Mathox all minerals rsg ns wr, the last all minerals rsg ns wr and many others that i forgot. Mods should think about this rule, since i have heard different opinions from every mod

You might be ok