In the "X-ray System Exposed" video at 1:08, Baraka activates his X-ray first, yet loses to the forceball once Reptile X-rays. This gives the impression that whomever activates most recently (Reptile X-raying second) takes armor away from his opponent.
However, in your "Sub-Zero Disables Armor" video around 0:17, Sub-Zero X-rays first. Cyber Sub-Zero then X-rays in the air, but is stopped by the clone. Now, this would make sense if Sub-Zero charged his X-ray for a few frames, in essense "activating" his X-ray at a later time than Cyber Sub. If not, this poses two conflicting scenarios - one where the second player to activate X-ray wins, the other where the first player to activate the X-ray wins.
Like I said, if Sub-Zero had charged his X-ray, it would possibly alter who the game considered to have activated X-ray "most recently." If you can, please test a quick situation with fully charging Sub's X-ray vs not Charging to see who the game considers to activate X-ray most recently, if this is indeed how the armor-stealing property works. Also consider that who the game considers to be armorless as X-rays clash may work similarly to how the game gives random priority to one player should two normals clash.
Edit: One note about testing Baraka's X-ray vs a forceball. Are there any start-up frames on his X-ray prior to the armor activating where he may be vulnerable? If so, try a situation where Baraka activates as late as possible without Reptile counter-Xraying to make sure Baraka isn't simply losing to the forceball by itself. On a few occasions playing Sub-Zero, I X-rayed on reaction to projectiles thinking I would armor through them, only to lose and have my X-ray stuffed. I learned Sub's X-ray requires a few activation frames before he is considered "armored," thus explaining why my X-rays lost on reaction. I'm sure you're aware of such situations and know which X-rays require time to activate armor. This is simply something I do not want you to overlook during experimentation.