While there is apparently serious evidence to the use of chemical weapons
Who gives a fuck about the use of chemical weapons? No one. The point here is the rebellion against authority, not the event. The absurdity of the whole concept of "oh you can line your own people up and mow them down with machine gun fire THAT'S fine, just don't use gas" should be obvious. Clearly it isn't.
While I somewhat agree with what you're saying in terms of semi-arbitrary "rules" in play, it's not just fine to line people up and mow them down with machine gun fire. In fact it's a war crime whether the targets are civilian or military. Now whether it's as likely to generate the same outrage? Who knows. I suspect about the same probability.
Clearly using chemical weapons to inflict pain and suffering is magical and very very mean in a way shooting people in the face or dropping fire on them isn't. World War 1 was a loooong time ago. The terror of symmetrical attrition warfare carried out using mustard gas or the like is an imaginary horror. Sanction nation states for killing large numbers of people, not the methods they choose to accomplish that.
I think the point is that we allow small arms and targeted munitions in warfare because there's at least the illusion of an attempt to minimize casualties among non-combatants. Large scale bombings tend to be frowned upon, but can still at least be argued as "it's a physical explosive and we really did try to hit that munitions factory and not that hospital next door". When you drop chemical weapons in an area, it hits everyone in the area, whether outside holding a weapon, or hiding in a bomb shelter. In fact, I think the primary rational for banning chemical weapons in war was precisely because while they're not actually that effective at killing people who are outside, on top of hills, driving around in tanks or jeeps, or otherwise actively engaged in fighting, they are incredibly good at seeping into low lying enclosed spaces, which is where civilians and wounded people tend to hide out whilst the battle is raging outside.
Fair or nor, overreaction or not, the leaders of the civilized world saw what happened when relatively primitive gas weapons were used in proximity to soldiers in low lying trenches along the front lines in WW1, realized instantly what would happen if they were used in an urban area, and decided to ban them. And they were almost certainly right to do so. Our rules of war, as silly as that sounds, are ultimately designed to allow party's to a military conflict to fight, while attempting to minimize the number of civilian casualties. They are not perfect, but they're better than nothing.