The PSP doesn't record the video (though, you could do that as well, the game plays far far FAR from real time... used it to capture some animated GIFs). It streams the data through USB... The Wii USB ports aren't even designed to be hooked directly to a computer so that cuts that option out. The only other options then would be to use a hardware device like USB gecko... but that only lets you capture stills.
If you want video then and are willing to pay for additional hardware... just spend some money to get a video capture card for your PC. I just picked up a real cheapy on Newegg for $20 and it works great even if the colors are a little washed out. Spend a bit more and you can get something a lot nicer.
