You may have figured this out already, but since no one has responded I thought I would chime in.
I don’t know if there is a specific way they are meant to be used, but as you already mentioned in your post, they provide a way to assign metadata to tags themselves (which are ultimately nodes anyway). It all kind of depends on how you use tags.
It looks like you are using this template, which you mentioned in Confused about tags inside property values in db version. I don’t know how that template designer leverages tag properties, but there are lots of possibilities. It is also worth noting that even properties can be given metadata/properties of their own. One way I am using this feature is to designate properties that are the inverse of a given property (which is used as a typed link, such as “cites/cited by” etc.). This makes it easy to display the right link label for a relationship depending on which node is the subject or object (without having to manually input the link both ways each time). Of course, to make this useful it is necessary to write an advanced query (which I have not really done yet 
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