Some details from the comment thread at Reddit:
Professional contact juggler here. Just coming in to say that we are all immensely proud of Yanazo... we've all been passing around this video for weeks. This performance apparently won him 1st place at the Japanese Juggling Festival, an event populated almost entirely by Asian jugglers (so you know the kind of caliber he was up against).
It's not very often that contact jugglers win these sorts of things - for instance, the last time it happened in the States it was Tony Duncan winning a gold medal in solo competition with one ball in 1994.
Also, to make this thread more efficient: yes, we have heard of the Fushigi ball; yes, it is a scam (brought to you by a former Wal-Mart PR exec); no, those are not Fushigi balls in the video; yes, it is still a huge sore point with contact jugglers; no, we don't talk to the guy who did their marketing any more.
EDIT: If you're really really interested in this, especially how to do it, go join the www.contactjuggling.org forums!..
For stage performance I use a 100m "stage ball," just like Yanazo uses in this video. They're a soft plastic ball weighing about 200g, usually a little grippy and yes, perfectly round and balanced. They run about $15 and they're also the "industry standard" practice ball since you can abuse them pretty mercilessly (I have one that was thrown into, and rescued from, a campfire - it's ugly now, but rolls fine).
For close-up performance (street shows and walkaround performance) I use a 90mm acrylic (the see-through ball) because they have to be totally seamless if your audience members come within about 2 meters. I downsize my acrylics a little because they're really heavy, and with some of the really delicate manipulations a 100mm acrylic is just a little unwieldy. Acrylics are dangerous (because they're heavy - I've nearly killed a laptop with one) and fragile (you're out $40 if you drop it on the street).
You can get them from any shop that sells juggling gear - domestically I like jugglingstore.com, neonhusky.com, and renegadejuggling.com. If you're in the UK, oddballs.co.uk and if you're elsewhere, homeofpoi.com is good too.