Heat a grill pan over high heat. Lightly brush the grill with oil and cook the squid and shrimp until just cooked through, about 1 minute. Cut the squid into pieces and set aside with the shrimp.
Roll out the dough on a lightly floured surface to your preferred shape. I like to pull it out like an elongated oval, but you can make an octagon if you are feeling clever. Place it onto a parchment lined baking sheet. Spread the tomato sauce on the dough working from the center outward. Liberally cover the whole mess with the grated Gruyere. Arrange your seafood as you like it. Stand the clams upright on the pizza so that when they open in the oven, the "liquor" inside stays mainly in the shell. Roughly tear the fresh mozzarella and place that among the sea critters. Drizzle a little of the oil from the anchovies over the whole pizza.
Pop the pizza into the oven and cook until the cheese has melted but is not brown, about 6 to 7 minutes. Scatter the bok choy over the pizza and cook until the pizza is brown and crisp and the bok choy is wilted. You don't want the bok choy to dry out.