I was confused as well, but I think the idea is that he's using only graph paper and a straightedge without measurement. (or markings)
So he has to place points with integer coordinates on the graph paper, and draw lines between them.
So he has to place points with integer coordinates on the graph paper, and draw lines between them.
I'm pretty sure this is just the grid of rational numbers. Interestingly, this is a subset of the 'constructible' numbers. That is, the numbers that can be produced from a compass and straight-edge (without even needing a grid).