The intended way is indeed to use the firework launcher just on the right of the ninken standing still in front of the house, and the one on the beach to distract the other two. Based on your comments you probably already noticed it but, just in case, I have marked both on your picture - one is hidden by the roof.
For comparison, here is a screenshot taken from the ground on the right of the house.
When you hit that launcher, the ninken will turn in that direction for a few seconds, giving you the opportunity to make a run and grab the "small animal" near the boat.
One possible plan is to stand on the roof of the house like you did, place yourself on the edge so you can shoot both launcher with an arrow, shoot the one on the beach, shoot the one near the house and then jump and glide from the house to the dog you have to rescue before the ninken turns back to that direction again. This way you can waste less time on the way to the pet you want to rescue and you will be able to grab it while "Blade Pup" is still distracted.
As an alternative you should also be able to run from the side of the house like they do in this video. It is worth to notice that in this case they left this pet as the last one to rescue, so they don't have to worry about the three ninken to see them afterward - they will simply despawn as soon as the challenge is completed.