This illusion was actually discovered by a man called Richard Gregory who I used to work with in Psychology at Bristol. Sadly he died last year.
The reason it doesn’t look hollow is because our brain is so programmed to see faces, that if it sees something like a face it ignores other cues to process the face, so it ignores the movement in order to make it a face, rather than a hollow face!
In the reception of the psychology department at Bristol Uni there is a hollow face of Richard Gregory himself – in fact in that link you’ve posted the vid on the right is one of Richards, and you can see it here with commentary http://www.youramazingbrain.org.uk/supersenses/hollow.htm
Hope this answers your question – I love this illusion!!!
There are loads of illusions like this. Essentially they arise when our brain tries to fill in information about the world and what we have learned about it – like the fact that faces normally bulge outward not inward. There is actually a good explanation for the illusion in the link you sent. I’m not sure anyone knows exactly what happens in the brain when you see a visual illusion, but lots of scientists are studying this. Illusions occur most often when the thing we are presented with doesn’t have the strong cues that we would normally use to tell us about it (like no shadows to tell us about the shape of things).
An interesting question would be whether from birth the hollow face illusion occurs – someone may have tested this?! I would predict it wouldn’t because at birth you haven’t learnt enough about faces to know that they usually bulge outward.
Have you seen the ‘Gathering for Gardner Dragon illusion’ that is similar to the face illusion – you should be able to find it on YouTube.