Unfortunately I can't tell you how to do this specifically in Vegas, but I might be able to lead you in the right direction. The effect is called "Compound Blur" in Premiere and After Effects. How it works is, you have your footage, and then in another layer above it, you have a "blur matte" (you'd need to turn the actual visibility of this layer OFF, if the effect doesn't do that automatically). This matte is a black and white image, where the white-most parts tell the effect which parts of the footage to be the most blurry. Whereas any black areas won't be blurry at all. So if you wanted to emulate this particular example, you would make an image either in Vegas or Photoshop or whatever, with a radial gradient going from black to white, making sure that the black part is fairly solid. Sort of like this.
Using this matte, I can achieve the effect with a look like this.
Now, I don't know if Vegas even HAS this effect or not, or if it does, if it's called the same thing, but that should hopefully get you closer.