I'm guessing similar to the diamond blades and pads used to cut granite. The edges usually aren't sharp, the blades are usually pretty wide, 1/8" kerf, but they're encrusted with diamonds. The blades don't usually get dull, they just wear down until the diamonds are gone. The diamonds not the blade itself does the cutting. Once the diamonds are gone, the blade will actually start melting and stuff.

I'm thinking it's got abrasive material embedded in the outside of the chain links. I kind of doubt it's diamonds, because that wouldn't work too well for steel and other ferrous metals, but it might be CBN or similar.