Yes, it’s a game. You have to play it, it can be completed, therefore – it’s a game. FACT.
So you “play” it by walking around with your 3DS hoping to bump into other people who have puzzle pieces you don’t have, or use the “coins” accumulated from walking to buy random pieces. Eventually, with luck and sore feet, you get all the pieces for all the puzzles. Like I did today! Yay!