The pedals look like SPD (or maybe Wellgo or Ritchie ... they don't look quite like my SPD pedals). But if you go into a shop and ask for MTB pedals or cleats, they'll ask you which kind you'd like ... there are several.
Just to add to your confusion, I ride with SPDs, and Rowan rides with Time Atak (not quite sure of the spelling) and both are MTB pedals but are quite different. And we both ride road bicycles ... we just prefer the MTB pedals and shoes.
So, you'd want to take your pedals into a shop when you go looking for shoes and cleats.
Generally you buy the shoes, and then buy the cleats separately. Occasionally the cleats will come with the pedals.
2 bolt are usually more MTB type cleats (like SPD), and 3 bolts are usually road bike type cleats (like LOOK).