I baked cookies last night and they came out rather crumbly. It felt like I put in quite a lot of flour - would that affect the crumbliness?
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 creaming, 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 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.
Too much flour can definitely cause crumbliness. I suggest you experiment with the amount by trial and error. This (alone) may not be the most effective solution though...
Moreover, the lack of eggs in that recipe is naturally going to have its effect. Egg is used in baking primarily as a binding agent, and the lack of such here is going to lead to lack of cohesion/increased crumbliness. If you don't mind adding eggs, this is the easiest solution. Otherwise, there are alternative binding agents that could do the job pretty well:
Cornstarch and water
Soy flour and water
Flour, vegetable shortening, baking powder, water
The recipe you give seems to utilise baking powder and vegetable oil as binding agents, but this is quite possibly insufficient. Also, I have heard that using whole-wheat flour decreases crumbliness.
There is a great page on Egg-Free Cooking Options in general over at exploreveg.org, which mentions the above options and more. (And gives exact measurements.)