I agree with the views here that this would not be a satisfactory substitution - not least because we add almond meal to a recipe to keep it moist, but two cups would make for a very heavy sad outcome. If you are gluten intolerant I suggest you try some of the pre-made gluten free mixes available, or make up a supply of your own...
I've been exploring gluten free baking (I have two new friends with celiac disease), but I'm no expert. That said, I think it would be a mistake to substitute 2 cups of AP flour for almond flour in this recipe. Almond flour is really just finely ground almonds. There's no gluten to hold it together, and between the olive oil in the cake and the oil in the almonds, I think you'd have a big oily mess on your hands. One of the ways gluten free cakes get height is by beating the egg yolks well to incorporate air into them. This recipe has you simply stir the eggs. So you'd have a flat oily mess. There are gluten free flour blends on the market. Bob's Red Mill, King Arthur, even Betty Crocker make them. I think you'd be better off using them--they have been developed to have as similar as possible properties as AP flour and would be safer substitutes.
p.s. after reading your recipe, i am wondering if david l. is right. This olive oil cake has baking powder and soda and separated eggs, so i'm wondering if maybe the almond flour would make the equivalent of a nut torte, which traditionally has little to no flour. If I were you, I would try doing a search for 'almond flour' on the 52 Recipes header; and do more google searches for 'almond flour cake' and compare those recipes to this one. Are you wanting to do this because of a gluten allergy? if so, you could certainly use some other flour substitutes, maybe in combo w/ the almond flour.
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http://www.davidlebovitz.com/2014/01/almond-flour-faqs-almond-meal/
Best of luck.