Because the DARPA video is self-explanitory, government-related, and an impressive feat of technology. 118's unveil video is only the last of those three. Random Joe not knowing what FIRST is or what Ultimate Ascent is would think that video is cool, but wouldn't really understand what was going on. They didn't have to design and build a robot to play this game in under 6 weeks, so they don't appreciate the amazing engineering behind Apex as most of us FIRSTers would. Just by watching the DARPA video you can tell it's about a robot moving in a life-like way, and any random Joe and their grandmas can see that and understand it. Also, DARPA being a government sector raises popularity amongst American civilians who are interested in what our government is doing.

tl;dr: The DARPA video is more popular than the Robonauts' unveil video because people understand it better. The minute we can get a video about FIRST that's self-explanitory and interesting, the minute we get a video shared and enjoyed by random Joe and his grandma.