The sound quality of the clip makes it pretty hard to get a detailed account of anything tone-wise. However, the sound of the guitar doesn't appear to be anything too difficult or expensive to achieve with regard to equipment. I hear a basic clean and a basic marshall-esque type high gain distortion at times.
From what you've listed, the quality of your equipment isn't an issue. You have some great gear. However, if you like high gain distortion, the "type" of gear your have may be an issue.
Your Boss DS-1 and CS-3 combined might get you there. However, the Peavey Classic 30 doesn't pack much punch in the area of high gain distortion. If you like higher gain distortions you might want to consider a multi-channel amp that has a preamp section designed for that sort of thing. The Classic 30 is not such an amp. Also, with the right preamp or distortion pedal, EQ will play a significant role in shaping the sound you want.
The Boss Metal Zone pedal might give you decent high gain results in front of a cleaner amp like the Classic 30. I've never used one. However, I'm sure someone around here could advise you on that.