How is this position a checkmate? In the photo below, it does not appear that I have the black king under attack. The next move that I made was my white queen to d8 and instantaneously I was told I had won by checkmate.
How is this possible in this situation as I don't believe I had the king in check prior to that move?
No, the Black king is not checkmated in the photo, but it will be on the next move if you move your queen to either of the squares indicated by the arrows (i.e. to c8 or f7).  Qd8# would also work.  This is because all of the black king's potential escape squares are covered by your men in the case of Qc8# or Qd8#, and of course there are no potential escape squares after Qf7#. The opposing king doesn't have to be in check before you make your move for it to be a potential checkmate.