Your description of your calculation already lets you count how many directed graphs there are. Between each pair of points, there seem to be 3 possibilities - no edge, an edge directed one way, an edge directed the other. You can count how many pairs of points there are - n choose 2 - points. So you've counted
However there is another definition of simple graph that doesn't allow for directed vertices. If so, your calculation overcounts because there's only 2 possibilities - no edge, or yes, there's an edge.