Part of what made the printing press work was the metallurgy required. You needed quality iron and steel for the screws and the typefaces, brass and bronze would not endure the stresses. Those metallurgic advancements largely came out of war and the need for metals that could handle black-powder explosions.
Even Gutenberg's primitive press, which was built out of a wooden wine press, was revolutionary. It used cast lead type. The Romans had lead technology.
While the printing press is probably required for industrialization, it is not sufficient. Your point about slavery holding it back is a good one.