That Aeon Magazine example looks like they tried to use radio boxes and couldn't figure out the HTML to do it properly and gave up.

Now, I just made the mistake of looking at Aeon's HTML source and its fine, but definitely some strange bugs (label for not matching input id is one obvious thing where someone failed some basic HTML SAN checks).

This is part of a larger problem where management doesn't listen to the coders/designers about UX issues.

Aesthetics often win out over UX or keeping the code base maintainable because management doesn't have to deal with the code and rarely use the website themselves to see how terrible the UX is.

It actually depends on how well you do it. ionic framework uses round checkboxes and does it really well. http://ionicframework.com/docs/components/#checkbox