The sample video most likely uses After Effects with an RGB channel separator linked to the song by an expression script to automate the effect.
For Vegas, there's probably a plugin that will help do it more efficiently, but there's a way to do it manually with a little bit of effort.
First drop in your clip and duplicate it twice so you have three tracks with the same clip stacked on top of one another. Set the composting mode for the top two tracks to "Add".
For each clip, use the following fx chain:
[b&w][channel blend][color curve]
The B&W is to set it to black and white if it already isn't. You can also use another channel blend to get better results, but use it in place of the B&W in the chain.
For the channel blend in place, set each track to either "Red Only", "Blue Only" or "Green Only".
Use the color curve on each clip to crush and remove the color from the blacks.
Then use the pan/crop box of each clip to adjust the X axis and offset the color channel of each blend. Use keyframing to animate them. You can use super sampling and motion blur envelopes for motion blur, but it'll probably get pretty CPU intensive.