You can shoot with both eyes open with iron sights too. Closing your other eye is good only in a long range fight when you need to see your front sight as clearly as possible and shoot with maximum accuracy.
There could be an effect for this case too and when you use focus (defaul shift in the keyboard) the character could change focus to front sight! It would be very realistic and cool!
This should be optional, something we could enable or disable in the menu. Nobody would unpleased.
Overall good video, but partially misses several key points.
In real life non-magnifying optics have a number of advantages over iron sights. The biggest one for me personally is that they're just simpler. They don't require different elements to be aligned, proper aiming involves only putting the reticle on the target. It makes target acquisition easier and much faster. The aiming reticle is also projected in the plane of focus of the target, not the rifle. When shooting with iron sights the proper technique is to focus on the front sight, leaving both the rear sight and your target blurry. Most optics don't have this issue, and you can see this in the video really well - the EOTech reticle is blurry when the camera is focused on the optic itself, and comes into focus as the camera focuses out towards a target. This makes accurate shot placement on targets much easier, especially at longer ranges. They're also low parallax, which means you can fire accurately when your eyeball isn't perfectly behind the sight - which is very useful when firing from behind awkward cover.
Most of this is stuff that's either not easy to model in a video game, or is intentionally not modeled because it would annoy the crap out of most players. It does lead to the slightly weird situation where many players prefer iron sights over the red-dots, even though in real life optics are better in every way.
Pretty much any aiming device can be used with both eyes open. In fact, it's widely considered to be preferable to shoot with both eyes open at all times. With iron sights and all optics up to the middle power range, shooting with both eyes open is better in every way. You retain peripheral vision and depth perception when shooting with both eyes open. Once you start to get into higher power scopes and longer distance shooting, keeping your weak eye open becomes less beneficial. Still, many professional long range shooters prefer to keep that eye open, simply because it's uncomfortable to keep one eye closed for long periods of time. You can get shooting glasses with one eye blacked out, or a lot of shooters simply put scotch tape over one eye of their shooting glasses to blur the vision out.
Still, the ultimate point of the video is a valid one. To be realistic, the optics, iron sights, and even the body of the weapon should be less present in the field of view. I'm not generally a fan of the transparent optic look, I find it looks campy rather than realistic, but the final version he shows in the video is pretty decent. I wouldn't mind seeing it in Sandstorm.