That's why you should enable two factor authentication on your credit card: online transactions would require confirmation with single-use password you receive by SMS.
I used to work in e-commerce and my company simply disabled the SMS protection because it would harm sales and the platform would sometimes completely crash.
On the other hand there is no way (that I know of) that I, as a customer, could prevent my card being used in non secured websites. So this system makes legitimate purchases harder and doesn't prevent fraud.
We need a different technology than credit card for online payments, they are not secured enough and any layer of security that we add around them won't work.
Make a purchase, then sign off on your phone (or fingerprint reader on your laptop).
It obviously won't resolve the issue posed in the article, but it is definitely a step in the right direction and many of the major CC companies are integrating more and more. In five or six years I can easily see Chase and the like giving an option to only let the physical card be used in chip-and-pin mode and to require the use of an approved service for any contactless/online orders.
Obviously the approved services thing is a concern, but not a huge one.