Smothered Mate or Not?

Is this considered a smothered mate or not? 

I was "called out" in another forum for referring to this as a partial smothered mate (I don't know if such terminology even exists) and not just simply a smothered mate.  My reasoning is that there is an empty square adjacent to the checkmated king.  The typical smothered mate has no such empty square.

Feedback would be most appreciated.  Thank you in advance.

that is suffocation mate

Sort of I guess.

That's a radiation mate, but with a horse:

The radiation coming from your queen, limits the enemy king. or eclipse mate (king queen and queen, being earth moon and sun)

I think to help you with the question, you need to answer other questions that are probably solved, what do you call these:

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I think that 'not having squares literally - all occupied by friendly pieces, is the same for a king as not having squares to go to. So your example is a regular smothered mate. smothered mate + pin.

Sometimes, pieces has negative values:

The queen is 'minus infinity' - it helps the mate.. It's all a matter of position.

I suppose my example would be better defined as an atypical smothered mate rather than a partial smothered mate.

Should be a suffocation mate like you and John have noted.

Smothered mate is a proper subset or special case of the suffocation mate where all the squares of escape cannot be accessed due to blockades by friendly pieces.

But this would mean that the classical back-rank mate could be classified as a smothered mate.