If the sound is a ujoint, it's probably too far gone for grease to do much, but obviously isn't going to hurt to add more. When I was keeping mine greased pretty regularly, they just had some play but weren't making noises or any vibrations, really.
Agreed, that particular video sounds like a ujoint to me. My rears gave out last spring, one particularly bad, and I had an almost identical sound - also mainly slower speeds, at slack throttle (coasting), and could hear it "ping" real quick when I pressed the gas and put a load back on the...