This article tries to narrow the definition, but not to exclude shoes, but to purify the discussion and how I think they should be described.
I believe minimalist shoes can be described in three words; closest to barefoot. So I would describe true minimalist shoes with a different term; "barefoot-style shoes." If you listen to some manufacturers their definition is much broader. I don't believe that the manufactures can define this category in this case. I think it needs to be defined by healthcare professionals. Interestingly they probably wouldn't define it as a category at all. They would say that whatever shoes you buy should be comfortable, non-restrictive, as close to bare feet as possible while still maintaining some level of protection. If it were possible, they would probably recommend going barefoot as much as possible, particularly for your kids.
It's all about maintaining the health of your feet as you age. In our younger years our feet are growing and need to be free and unrestricted so that they can grow properly. In those years we probably go barefoot much more than we do as we get older. Once you're grown it's just as important to go barefoot as much as possible, but life interferes and it isn't always convenient or desirable.
What is the theory behind barefoot-style shoes? It is that our body provides all the cushioning and stability we need for walking and running barefoot without the added weight of shoes. So, barefoot-style shoes try to approximate that condition by being very flexible and basically flat with zero incline from front to back. They also allow your toes to spread out like they do when you're walking or running barefoot, while providing some protection from life's intrusions like stones and sticks. Even though they do provide a layer of protection, they also give you a feel for the ground that you cannot get with other shoes and are typically very lightweight. If you are not already, you should be aware that there is a whole movement around running in bare feet that is also very popular though adding a little extra "skin" for the rest of us is probably reasonable.
That's not to say that immediately switching to barefoot-style shoes is the best approach, particularly for runners. If you're not used to going barefoot, then barefoot-style shoes will take a cautious and pragmatic approach to adapt your walking or running style. Barefoot-style shoes force walkers and runners to go back to basics and adapt to allow their feet and legs to provide primary cushioning and stability. Many say though that once they've gone barefoot-style it's hard to go back!
This article is not designed to advocate barefoot-style shoes, but just to put it forward a brief opinion about how to describe them as part of minimalist shoes. I do suggest going barefoot as much as possible and to keep your feet unrestricted and healthy. You should also consider trying, with your healthcare professional's advice, a brand of barefoot-style shoes.