The short answer is, it is called none of those things. An edge index is not quite the same thing as your other examples (Table of Contents and List of Figures).
Take a Table of Contents for example.
Table of Contents
Chapter 1.....page 1
Chapter 2.....page 15
Chapter 3.....page 32
This is called a Table of Contents because it graphically looks like a table, and it displays contents. Therefore it is a table (in the graphical/mathematical definition of the word) which contains contents. A simplified way to describe a table which contains contents is a Table of Contents.
This is slightly different than an Edge Index. Mirriam Webster's definition 2A for "index" defines it as:
a list of items (as topics or names) treated in a printed work that gives for each item the page number where it may be found
Now, that means that by calling something an "index" we have already established that it is a list. Anything which is an index does not also need to be called a list or a table; the fact that it is a list is implied by the word "index".
In the specific case of an Edge Index, it is an index (a type of list) which appears on the edge of a book. Edge is just an extra adjective to describe the index, which we already know to be a type of list. So it does not need to also be called a table or list; it is an index. The words Edge Index speak for themselves.