I Think You Know This Part Already
Okay, so ordinarily what you're watching on a 3D TV is 3D content. That is, each eye is fed content filmed from a slightly different angle to emulate depth perception. Thus, your TV needs to be capable of showing two different images simultaneously. 3D televisions already do this, it's built in. What the glasses do is filter the content so that the left eye sees one image and the right eye sees another. This is done with polarization and there's quantum physics involved but I won't get into that. It's not important.
The Really Simple Explanation
Instead of polarizing the glasses for two different eyes, you polarize them for two different players. Thus, player one's glasses are both polarized one way and see one image, player two's glasses are polarized the other way and sees the other image. Essentially, player one and player two only get to see a 2D image but in return they get to play from the entire width of the screen.
What I don't understand is why Sony is charging so much ($69) for extra glasses. Polarized lenses are cheap! Maybe it's the tech that allows the lenses to change polarization that costs so much... No, that's also cheap. You're paying Sony Tax for those glasses. If I had a Sony 3D TV and needed new 3D glasses I'd just make my own from those you get at the movies. These ThinkGeek De-3D Cinema Glasses sound like a real bargain at 14.99. They only sell them polarized for the right eye though. Perhaps if the TV takes off they'll consider left polarized versions.
Do I Need a New TV?
Highly doubt that. Any 3D TV already on the market can do this. But the glasses that came with it are probably polarized in only one way like the ones you get at the theaters. Nobody anticipated a need for the ability to change polarization. Again, you can just make your own pair from the cheap glasses they give out at 3D movies.
It's a rather brilliant use of a 3D display, actually. And hindsight being what it is I now wonder why it took so long for us to get this.