... there is a way of telling. You click on one of the products and get to a subpage and look at the URL - the php programme the guy is using is ... PHP! As for the database - it is in all likelihood MySQL, as Ravenous said.
Btw - trading laws vary drastically from one nation to another, but the Matrix Shoes site would be seriously illegal under European law (no contact address, no e-mail, no statement of liability, no terms of sale, no statement to the effect that the site is just an advertising front for Zappo Shoes ... the list goes on). The owners of this site would land up in court quicker than you can say "EU trading regulations" ... but I guess other continents are not so bound up in red tape.
Best o luck
Norm