That's my video
That tone is partly the bass (Ken Lawrence), but I think the strings are a big part of it too. TI Jazz Rounds are the only roudwound string I'm using on electric basses now. They really do have a unique and special tone and feel. They're the only roundwound string I've played that doesn't have a super bright, zingy tone (which I hate). Right out of the box they have a very warm and organic sound. They also have a very light gauge (low tension) which feels perfect to me. Smaller windings as well, so they have a smoother feel than other roundwounds.
They are expensive, but definitely worth it to me. I generally get a new set every 4-5 months if they're on a bass I'm playing regularly. Here's another vid I just did last week
http://www.youtube.com/watch?v=LXceSuYEn9o