All Orc traits (and Frenzy/Counterattack, which function the same) include damage to life or armor as a trigger condition. This was an intentional change in version 3.4.
So, this is the part that is inconsistent with other game mechanics. “Destroying” armor (via a Manglike, Megavore, Grave Knight, Bone Dragon, Golem, armor stat reduction from Plague’s trait etc…) does not count as “damage” in the way that the rest of the game defines “damage” - barrier does not interact with it at all. However, the description of how the traits were changed in 3.4 leads me to believe that this it is intentional for armor reduction/destroy to be considered in triggering these traits as it specifies “damage to either (specifically) Life or (specifically) Armor” as a trigger condition, and “damage to (specifically) armor” can be interpreted as reduction or destruction of armor, as you have stated. It is just conveyed poorly through the description (like many other things).