These work simply by digitizing and capturing the input signals, then multiplexing the digital signals with a shifting DC bias so they display like a logic analyzer. You can totally duplicate it, and I've seen articles in the past for such projects. I didn't catch the price, so I can't say it wouldn't be better just to buy it.
Keep in mind that each signal stream is a new trace on the o'scope, so you will probably get flicker. That is one inportant way it would differ from a 'real' logic analyser. It should also in include a couple analog channels to be a complete tool. If you're looking for a simple logic analyzer, give the USB units a good look too.
Awhile back, someone linked a project for a logic analyzer using a uController development board. My idea is to use an FPGA dev board and USB to make a logic analyzer, just so I can say I made it myself. That is, if I ever get enough time away from work so I can work on my projects.