I can't see that article, and I'm sure there are others as well... However, this isn't entirely new, I've read about experiments with this kind of material before.
The idea is, that inside the material is small bubbles with 2 kinds of liquid. 1 kind for filling out the scratch, and another kind for hardening the filler.
When the material is scratched the 1st liquid will run out fast and fill the scratch, and harden quickly afterwards. Very neat, but it's only good for very small scratches.
Besides, I question it's validity when used in combination with transparent materials, but you never know...
You can indeed see the New York Times article. All you need do is register and it's Free. Oh yes, about once a month you may get an email from the paper (you can ask to be removed).
This is a pretty cool technology, but I don't see how it could be used well with DVDs. If a DVD is cracked then more than likely the aluminum layer (where the information is actually stored) is damaged beyond repair. And if it is a scratch then repair would be extremely difficult. Sure you could fill in the the scratch with new material, but as I've found in the past, surface finish (particularly surface flatness) is extremely critical to DVD performance. I can't see how a self-fixing plastic could fill in a scratch and fully restore the original flatness.