Put the rice in a fine-mesh sieve and rinse under cold water, stirring with your hand, until the water runs clear. Shake well to remove as much water as possible. Set the sieve over a bowl to continue draining, 5 minutes.
Transfer the rice to a medium saucepan and whisk in 1 3/4 cups water, the matcha and 1 teaspoon salt. Bring to a boil, then immediately reduce the heat to low. Cover and cook until the water is absorbed and the rice is tender, about 20 minutes. Remove from the heat and let sit, covered, 10 minutes.
Meanwhile, cut the seaweed snacks into matchsticks with kitchen shears. Mix the vinegar and sugar in a small bowl until dissolved.
Fluff the rice and gently fold in the vinegar-sugar mixture, pickled ginger, scallion whites, sesame oil, 2 teaspoons sesame seeds and salt to taste. Divide among bowls and top with the seaweed snacks, scallion greens and remaining 1 teaspoon sesame seeds.