The “category” concept is auxiliary and used to make various definitions shorter. For example, the content model of several elements is “flow content”, and though the category name is somewhat obscure, the concept still makes the definitions much shorter and more understandable than repeating a long list of elements.
The word “category” may be misleading, because an element may belong to more than one categories. However, the word “class”, though more descriptive, might have confused the concept with the concept associated with the class
attribute.
There is no name except “category” for the concepts in the drafts cited. Outside the drafts, you can use, if needed, an expression like “category of elements as defined the HTML5 CR dated 6 August 2013” or some looser phrase like “category of elements in HTML5”.
Calling the categories “functional”, “structural”, or something else would mean taking a position on their “true nature”, and usually a wrong one. The categories are formed for different purposes and on different grounds. As said, even the word “category” may be misleading, and the drafts don’t actually use it in the heading for the clause that defines the “categories”. Note that the clause, 3.2.5.1 Kinds of content in HTML5 CR, says, after mentioning some categories: “Other categories are also used for specific purposes, e.g. form controls are specified using a number of categories to define common requirements. Some elements have unique requirements and do not fit into any particular category.”