first of all thank you for compiling a QotD.
However, I do not quite agree with the solution.
'Unique' is just taking the definition of a clusterd or non-clustered index a step further.
'with included columns' and 'filtered' again are non-clustered indexes (with advanced features).
So I don't see them as individual types, but sub-types at best.
Hence it comes down to 5 types (why I got it wrong):
I assume, though, that this is another wording issue ;-); nevertheless an excellent lesson having to recap what index types there are.