Well, looking at the recipe...
The sugar (brown sugar + honey) level looks roughly appropriate compared to the flour so that's unlikely.
The fat level looks a tad low for the cookies I normally do, but I've never used oil in cookies before. You might try increasing the oil just a bit to lend extra tenderness, but I don't think this is the real issue. (Using oil in cookies also means you're not creamingcreaming, which is typically important in most cookies...so its a bit odd, but I don't know that it would cause them to be 'crumbly'.)
The lack of the egglack of the egg definitely isn't helping it to keep structural support. The recipe is basically banking on the fact that it needs to be moist to hold together. There's not really enough liquid to form gluten to add structure (which you don't usually want for cookies anyway). Since there's nothing in the cookie to give it 'structure', if you dry it out its just going to fall apart on you.
I suspect your problem is from the directions of 'Don’t overbake these, or they’ll dry out a little.' They dried out a bit too much and lost all support. It's easy to over bake cookies and this is a recipe with very little room for error in that area.