Changing a vegan cookie recipe?
There are a couple of things in that recipe that appear to be used as an egg replacement:


Pumpkin puree - usual rule (as far as I'm aware) is to use 1/4 cup per egg. This is particularly good for adding moisture, so reducing this would be a good start. Baking powder can also be used in conjunction with this to leaven the mixture.
Coconut oil can also used as an egg substitute in the right context. Honey (or, as this is a vegan recipe, maple syrup) can also be used in conjunction with this, as can baking powder. However, baking powder and to a lesser extent, honey/maple syrup could still appear in a recipe before the egg has been substituted.


All in all, my suggestion would be to first reduce the amount of pumpkin puree (or possibly even remove the pumpkin puree entirely).

An alternative (although possibly a less effective one) to this, or if removing the pumpkin puree doesn't manage the job, would be to cut down on the amount of coconut oil. As you've mentioned that you like maple syrup, cutting down on that would be the last resort.

There is a question of whether the baking powder is also used to help with the lack of eggs, but baking powder often appears in recipes with eggs as well, so qualifying whether or not to get rid of baking powder is more likely to be dependent on the flour (self raising or not) used.