I watched the video. That is not my preferred method. He's lazy and working harder to be lazy. Not relevant to your front issue, but remove the bolt at the front of the brake tension arm for the rear caliper and lift the arm off the mount point. This makes it much easier to lift off the rear caliper off the rotor and set it aside when doing the rear and you're not fighting the caliper when removing the wheel.
On the front, take the time to remove both front calipers. It's just silly to fuss with one caliper and it's very quick to remove both. That makes re-installing the wheel so much easier too. Besides, it's a good time to inspect your brake pads as well. BTW, 19mm is almost exactly 3/4" , (.748" Vs .750"). 3/4" is sometimes easier to find. Many spark plug sockets have a 3/4" hex on the back side as well. Removing the rubber insert and inserting an extension in backwards allows the spark plug socket to be used as an Allen socket, (if the square drive hole goes all the way through).
I also noted that he neglected to show his re-installation of the wheels. And I'm sure he struggled a bit with that, having one caliper still on and not disconnecting the brake caliper tension arm in the rear, or simply took care of those things before or during his re-install.
The guy does a nice job of talking thru everything and kudos to him for putting it out on the net. But you can really tell it's his first time doing the job on the Super Ten. He's not prepared and he offers some explanations for things that are slightly off, as if he doesn't quite understand why, but has been told that by someone else. Example, you don't touch the brakes because it will push the pistons and therefore the brake pads out and make it impossible to put the caliper back on the wheel w/o retracting the pistons first. The only way you could get air in the system from that is if you completely pushed the pistons out of the caliper. That takes more than one squeeze of the lever or press of the pedal to do that. (several required)
If you really did push the right caliper pistons in after releasing the bleeder valve, did you then bleed the brake system afterwards to remove the air from the system? You didn't need to release the bleed valve. The fluid will just go back to the reservoir if you don't and no fluid is lost.
I should have asked this before, but why do you believe the piston sticks? It's completely normal for pistons to come out unevenly when no pads are in the caliper and you squeeze the lever. Do you feel it's sticking 'out' and dragging? If that is the case, one rotor would get hotter than the other and this should show up quickly with a heat effected rotor.
If you removed the right caliper, why do you feel damage my have occurred? The pads are still in the caliper. The piston is unlikely to be damaged from any of that. Worth noting, the most common error during wheel changes or caliper removal/installation is just getting the caliper back on with both pads on one side instead of with the rotor between the pads. It happens to the best of us.