My DH has a nut allergy, so I can't use almonds either.
You can successfully substitute the things the others have suggested like flour or different types of ground seeds for almond meal, but I've only done it if the recipe asks for a small quantity of nuts.
In this recipe almond meal is the main ingredient. It's used instead of flour. Personally I would choose a different recipe for a chocolate cake that uses flour and not make this cake. You could substitute and it might work, but then again it might not. I wouldn't risk wasting time, eggs, chocolate etc. but that's just me.