This site is the most legit site I've seen that is obviously a scam. They use PayPal and then UPS saying items were delivered and they just disappear into thin air leaving neither PayPal or UPS no way to say they are not legal. How do you shut a site down?
If you or the site are in the USA report to the FTC, also contact law enforcement but they may ignore it if the amount is small or there isn't a lot of complaints against them. You could report to paypal or submit a claim but you have to be wary of that as well as paypal often makes piles of money on fees from scammers but at least you have an option to make a claim. Another thing you can do to gather information is do an online search for their domain registration info with a whois search which is publicly available from many web hosting companies. At least you can probably find out who's running the site.