The travelling production gets around the problem of building a race track by using 3D film to show the races asking the audience to don 'safety goggles' during the race so that they can see the 3D effects. Possibly surprisingly this works really well. My main annoyance with the original production was that no matter where you sat in the theatre there were sections of the race track you couldn't see -- using a 3D film means that everyone now gets to enjoy all the action and the theatre doesn't have to be half destroyed!
The 3D effect is achieved using two digital polarised light projectors and a set of polarised viewing glasses. Here are the glasses from Starlight Express:
One of the advantages of using polarised light rather than the old fashioned green/red anaglyph lenses is that the film is seen in full colour with no colour bleeding due to even the slightest mismatch between the colours projected and those used in the filters through which the film is viewed.
Briefly the effect works by projecting two slightly different pictures onto the screen (so without the glasses at best the film looks blurry and at worse undecipherable) with each projector using differently polarised light. Each lens in the glasses only allows through light polarised in one direction so one eye will see the output from one projector, the other eye seeing the light from the other projector. The brain then assembles an image which appears to be in 3D. You can see this visually in this image reproduced from an informative article on How 3-D Glasses Work.
With the advent of relatively cheap digital projectors this method of showing 3D films has become immensely popular. I've seen one other film before using the technique at an IMAX cinema, in fact you can even go see the latest Harry Potter film as an IMAX 3D experience (if you are so inclined).
So we finally get to the reason the post title mentions cellophane. It turns out that in 2003 a researcher named Keigo Iizuka discovered a neat trick with laptop screens and cellophane. LCD monitors emit polarised light which means that when viewed using 3D glasses you can only see the screen through one lens, through the other it looks as if the screen is turned off. Now while interesting this doesn't allow us to do anything new. However, it turns out that cellophane can change the polarization of light. So Keigo Iizuka simply covered one half of a laptop screen with the right kind of cellophane to change the polarization of the light allowing 3D images to be produced. Full details of this neat trick (and a second trick using two camera phones) can be found in an illustrated example titled Using cellophane to convert a liquid crystal display screen into a three dimensional display.
Not for want of trying but I've yet to find the right kind of cellophane!