You could do it by attaching a mesh to the skybox, I was playing around with rain a while ago which works in a similar fashion. But the problem is it will be static in regards to sun movement, when the sun moves across the sky, the rays wont follow it. By the looks of those videos, he has done just that.
hmm, a thought just hit me,,, a shadow caster that is not rendered, casting a shadow texture (the sun rays) onto a transparent mesh set to receive shadow. Then it could be Dynamic. I might do a bit of a test actually, I considered making something like this myself a while back, but I got side tracked and never got around to doing it.