The idea behind the law was to make it hard to make fraudulent purchases. So everybody shopping on the internet is required to register with the government and get a government-issued certificate that can identify them to Korean sellers. On the surface, this sounds a bit invasive, but not catastrophic. The problem? The certificates only work through an Active-X plugin, developed by Microsoft. Since Internet Explorer is the only web browser that supports Active-X, it is impossible to make an on-line purchase using any other web browser.
Do you have a Mac or run Linux? You'd better have a Windows PC or a virtual machine running Windows, because without one, you aren't going to do any shopping.
Cell phones and tablets have alternative software that can support the certificates and permit shopping, but for some reason (that the article doesn't mention), no such software exists for non-Windows desktop/laptop systems.
And just to ice this cake with a great big layer of irony, this policy has had the result of making the internet less secure for Koreans. Because they have to shop with Internet Explorer, and have to approve the use of Active-X controls in order to make purchases, the population tends to use IE for all web browsing, and they often get into the habit of clicking "yes" whenever any Active-X control wants to install itself. Which opens their computers up to all kinds of malware - which wouldn't happen nearly as often if they were using some other operating system or some other web browser.