Hi Riley,
Sorry to come late to the party, but I learned from my kid last night that you have to have one of the newish Macs (the ones with Intel processors that can run either the Mac OS or Windows natively). It won't work on the older Macs regardless of OS version or Safari version.
My older aluminum Powerbook was unable to do anything with the NBC videos, but after he spent 10 minutes or so typing and downloading and installing stuff, he got the Macbook to play Olympic videos just fine.
FWIW, I just finished watching the US women vs Cuba quarterfinal volleyball match, and the Internet video experience was so superior to watching on TV that I hope to enjoy a lot of the Olympics that I wasn't able to see during broadcast. At least on this one, there was no verbal commentary, no cutaway breaks, no commercials. Just the action in the arena from the first warmups until the participants exited the arena at the conclusion. They showed useful stats in between sets (games), and overall stats after the match was over.
If the player allowed for full screen, it would have been magnificent. As it was, I'll settle for superior.
Don't know how long that archive will be available, but it is an awesome thing.
If you were already using one of the correct Macs, then I suggest you find a 12-25 year old to help you figure it out. That has always worked for me.
Best wishes,
Dan