It's pretty hard to find places you can order in Korea, or from Korea, that don't require a Korean phone number. There are services and stores that exist just to buy things from other places in Korea and reship or resell them to people both in and out of the country, just because people don't have Korean phone numbers.
Even online purchases like audiobooks often requires a local phone number.
They sure make it hard to spend for any non Korean to spend money.
And it's not every site, there are some huge retailers (www.aladin.co.kr for example) that do not require it. So it's got to be just that most websites never bothered to build a checkout process that works without a phone number?