Why is the inverted index called so and not simply index?
Here is an array:

A[0] = Alice
A[1] = Bob
A[2] = Charlie

Here 0,1,2 are indices.
Now suppose that we want to know which index contains a given word. Then we use a dictionary:

D[Alice] = 0
D[Bob] = 1
D[Charlie] = 2

This is an inverted index (according to your Wikipedia quote).

The word index has different meaning in different contexts:

Technical books often have an index of terms at the end.
The Catholic church held an index of forbidden books.
In economics, there are financial indices.
In computer science, an index is usually an integer used to index into an array.