You didn't follow the tutorial. Granted, it's a poorly written tutorial. Make sure you read everything, and you can ask a question in case the awful directions like "Maps: Reflection: Raytrace (REFMAP.gif)" don't make sense. I did a Google search for REFMAP.gif and found the image he was talking about. I did the rest of the tutorial and my image looks like his.
He also skips some steps, at least one that I can find. He very obviously turned down the shadow density of his light because the shadow isn't pitch black. You can do this by selecting the light, then on the right rail going to the shadow parameters section, and setting density to 0.5.
This tutorial is also a joke because he tells you to weld a bunch of cones together. What the hell? Not only is that an assanine method, but CONES? A cone with the same radius at the base as the tip is called A CYLINDER. Regardless, the easy way to model a chain link is to make a torus, right click > convert to editable poly, select the top half of the polygons, and just drag up. Viola`. A perfect chain link.
For reference, here's what I came up with following the tutorial. Applied a lattice modifier to the middle one, and put a small reflection on the floor:
