The article also said that one of biggest challenges with making 2D polymer was keeping it 2D without it going 3D. But there was no explanation why that would be worse.
Normally the molecules can only assemble in a chain. They can make solids in three dimensions by being long and making a big tangled mess. It's like extruding dough into spaghetti, then stirring it around to make a big tangled ball. Instead, they found a way to roll the dough out into an arbitrarily large flat lasagna-like noodle. Then they stacked them and found they stick to each other well and could make a much stronger material than the spaghetti ball. The only real limit being the amount of dough and a space to roll it out on.