The directions for this recipe don't include using the 2/3 cup oats. I omitted it and the recipe did not turn out well.

Yes, omitting the oats entirely would not have ended well. The oats were necessary to help make the base. If you wish to try again, add them after you've cut in the butter, so you end up with something more akin to an oatmeal cookie dough.

I haven't made these, but I would assume the oats would get mixed in with the flour before you cut in the butter, or possibly stirred in between cutting the butter in and bringing the dough together with your hands.