I reckon the noses in the examole images are on the wrong side. The images are cross-eyed, e.g. the left image is for the right eye. The nose on the left image should therefore be on the left, and vice-versa for the other eye.
You can test that by crossing your eyes so the images match and try focusing (the first try takes a while). If you see a stereoscopic image, the source is cross-eyed. If it were not, The depths in the image would look "weird", because they're inside-out.
With a VR headset, the left image is shown to your left eye, and the right to your right. Intuitively, it should be clear that they aren't cross-eyed, since your nose is in the middle of your face.
And as someone else said - you're crossing your eyes, when you should perhaps be doing the opposite - looking far into the distance until the images overlap.
Close your right eye, your nose will appear on the right of your left eye. Close your left eye, your nose will appear on the left of your right eye. They have this correct. When you put the goggles on it will seem the same as you currently see, the nose fades because it is on the far side of your vision field of view and on opposite sides.
I always wondered after seeing this a bit ago if the addition of a torso might also help. Part of the disorientation might be that it seems like your body is not there. A nose with a torso and eventually LeapMotion like hand controls/arms, may help reduce VR sickness.
It might appear like that, but it is about distance!
Moving the two images over each other will make your brain think the nose that is farest away from the common center is closest.
BUT: the nose should ideally be mirrored, so that the shapes match, at least if you want to combine the images directly using cross-eyeing. They are correct if you show each picture to one eye though (what VR glasses are doing), every eye sees what it would see. However, little differences are filtered out anyway from your brain, merely a disturbance.
I just tested it and it seems I can manage fusion and see the effect both if I switch them and if I don't. Now I'm confused. is there something special about these images in particular or has my perception been all wrong?
When I tested it out, I got the proper sense of depth perception when I looked at it correctly (i.e., looking through the plane of the monitor, with left image for left eye) and got no sense of depth perception when looking cross-eyed (i.e., left image for right eye). It's temping to think you're seeing depth as soon as the two images "snap together" when you're cross-eyed, but when I actually consciously checked I noticed that the images in fact looked flat (except for the nose).
As far as why it looked flat rather than inside out, I can only guess that that depth info conflicted with the other depth information you get from vision (parallax, known relative object sizes, perspective lines) and my brain ignored it.
EDIT: Actually, after trying the second view (the one with hands, not the roller coaster) cross-eyed, I saw the inside-out depth. It's most noticeable looking out the window.
