Using chemical weapons is already a war crime, so governments just decided that the chemical weapons they use on their own people are not chemical weapons. Tear Gas was the first chemical weapon used in World War I:
The military can't use tear gas on the battlefield; military police can use tear gas against rioting soldiers and sailors. Soldiers can't use hollow point bullets even in those calibers, like 7.62x51mm, where that is by far the most common type of bullet used by civilians because of its effectiveness in hunting; but police use hollow point bullets all the time, in part because they are more effective against unarmored targets (though less effective against armored ones) and in part because they are much less likely to pass through a wall and strike someone the officer can't see.
These differences are not due to governments deciding that tear gas is not a chemical weapon or that hollow point bullets are not hollow point bullets, but rather because the laws of war apply in war and not elsewhere.
If you were serious about the war crimes thing, you'd have to acknowledge the Antifa and BLM committed war crimes by not having uniforms and clear insignia and by not distinguishing between civilians and non-civilian property when destroying things during their raids. There is no such thing as a body of law that applies to only one side. Talking about war crimes in this context really is disinformation: it confuses what those laws are about as well as the difference between international and domestic jurisdiction.
It is probably this very general language that lead to the restriction of riot agents. Although they do not kill by poisoning or kill by asphyxiation, their method of operation certainly involves some combination of poisoning and asphyxiation.
The USA has tended to hold that riot agents are not what is technically called a method of warfare because they produce "...merely transient effects...", and thus do not technically fall under the terms of the protocol, but has also long held that they are not authorized for general use, either. Per a field manual from 1956:
It is the position of the United States that the Geneva [Gas] Protocol of 1925 does not prohibit the use in war of … riot control agents, which are those agents of a type widely used by governments for law enforcement purposes because they produce, in all but the most unusual circumstances, merely transient effects that disappear within minutes after exposure to the agent has terminated. In this connection, however, the United States has unilaterally renounced, as a matter of national policy, certain uses in war of … riot control agents. The policy and provisions of Executive Order No. 11850 do not, however, prohibit or restrict the use of … riot control agents by US armed forces either (1) as retaliation in kind during armed conflict or (2) in situations when the United States is not engaged in armed conflict. Any use in armed conflict of … riot control agents, however, requires Presidential approval in advance.
In Vietnam, riot agents nevertheless saw very wide application.
https://ihl-databases.icrc.org/customary-ihl/eng/docs/v2_rul...
Using non-lethal weapons like tear gas is not a lower standard of morality. Nor is using bullets that are less likely to pass through the intended target or the surroundings.
Military personnel are not actually held to a very low standard -- much lower than police -- when they are fighting unlawful combatants like citizens, because people who are not fighting as military personnel enjoy no or almost no protections under the laws of war.
Trying to draw a parallel here with the laws of war is silly.
But since many people share your view - that they're non-lethal and thus morally superior - these less lethal means are used frequently, and often inappropriately, when the use of force is not justified.
The parallel is clear: government funded and backed forces equipped with military gear, using military-developed weapons (chemical, sound, light, physical); some of which are restricted by international convention during war.
And there will be no trials to hold people accountable for mis-using these weapons; as pointed out in the article, the government is actively blocking such attempts.
It's not because there is tear gas that police are sent to disperse crowds. Without tear gas, they'd use some other non-lethal implement authorized for that purpose. Authorizing non-lethal force to disperse crowds is not holding police to a lower moral standard than that to which the military is held.
In fact, the military has the same kind of authorizations for dealing with (a) rebellious troops in its own ranks, (b) prisoners of war and (c) civilians in occupied territory. That is why the DoD does research on these incapacitating weapons. It's military forces that are held to police standards when these weapons are used, not the other way around.