Yay, wiggle effect! I've always wanted to shoot a music video like that. Just to mess with people.
Yes, it is just like a shaky video and certainly adds no more feeling of depth than a sweeping camera move does. However, it's an effective way of displaying stereo stills for people with little or no depth perception, as it does not require binocular viewing (just a whole heap of imagination) to "get" the effect.
This is one of my favourite wiggle shots ever, from NASA's
STEREO probes;

Also, I'd be tempted to align your avatar further behind the screen Lancer. Things that come out of the screen feel a bit uncomfortable, especially if they're touching the groundplane, because that in turn will touch the edge of the image and cause a "window violation" (where things in front of the screen touch the edge of the screen and the brain gets confused about how they're being cut off by somthing that's behend them). James Cameron routinely violates windows, but only with defocussed foliage. All a matter of personal preference and how much you think the audience is willing to forgive really. I personally find a bad window violation to be a jarring as leaving a boom mic in shot. Not that you have that trouble in CG.
Mainly I just wanted an excuse to pull apart the channels and realign it to answer your question from months ago. When I did this it exaggerated the jpg artifacting, because now I've shifted one eye over we're seeing duplicated artifacts. I'm thinking colour correcting ghosty anagylphs wouldn't cause this problem because you're not moving anything around. But, I've just realised there's not enough colour information within the anaglyph to recorrect it. I want the full colour information from the left eye to be able to average it, but all I've got is the red channel.
So no, we can't remix anaglyphs with no anaglyph colour correction, but we can realign them if we enjoy exaggerating compression artifacts.