First of all, let me be clear that I am no expert on gluten-free cooking. I have worked some with gluten-free flours that are primarily made from rice, but Bob's Red Mill All Purpose Gluten Free Baking Flour has a great reputation. I wouldn't assume that is causing you a problem.
Having said that, there were several things I noticed in the recipe you used:
(1) It didn't include salt - you might want to add like 1/2 tsp. salt.
(2) There was almost no ginger in the gingerbread recipe - for your half recipe, I would have used at least 2 tsp. ground ginger and possibly even some fresh grated ginger.
(3) Substituting 3/4 cup honey for 1 cup sugar would add a little liquid to your batter and a couple extra ounces of overall weight - probably not enough to weigh it down against the baking powder and soda that are in the recipe. I think you chose a solid substitution there.
(4) I think the fat content is woefully inadequate. Fats, at least with wheat flours, will tenderize baked breads by impeding the formation of gluten. I don't know how fats work in conjunction with gluten-free flours, but they provide a sense of moistness in baked wheat flour products and I assume they would have a comparable impact of gluten-free breads. In a comparable wheat flour gingerbread, I would have gone with 8 Tbsp. (1 stick) of melted butter rather than 2 Tbsp. oil. Butter will impart a better flavor, for sure. 2 Tbsp. of oil sounds like something from a pancake recipe, not a quickbread recipe.
(5) I don't think your recipe calls for sufficient flour to support the liquid ingredients in your gingerbread. I would recommend increasing your flour from 2 cups to 2 1/4 - 2 1/3 cups (even 2 1/2 cups wouldn't be outrageous). Using a little bit more flour will probably generate the greatest increase in fluffiness.
(6) Rather than baking the gingerbread in a loaf pan, I would recommend baking it in an 8"x8" or 9"x9" square pan. That much batter in a loaf pan can prove too much for any amount of leavening to handle. Having the batter spread-out over a larger area will make a thinner gingerbread, but one that the leavening can handle. Naturally, in a different pan, you would need to adjust your baking time to like 40 or 50 minutes - you can usually tell when gingerbread is done by seeing that the sides have pulled away from the pan and a toothpick inserted in the middle comes out clean.
I hope that isn't too much response. I wanted to be as clear as possible. Basically, more flour, more butter, more ginger, and more pan would be my recommendation. Hopefully a gluten-free expert can weigh-in to cover any considerations I don't know about.