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
VegetableFlour, vegetable shortening and, 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.
If you are a vegan, thereThere 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.)