I've made that cake, but it's been years ago. As I recall it is a very moist cake and delicious. I pulled my older cookbooks and found a number of recipes for Raw Apple Cake, with a few variations. My recipe:
Raw Apple Cake
2 cups sugar
1/2 cup shortening
2 eggs, beaten
1 tsp. cinnamon
1/4 tsp. allspice
1/4 tsp. nutmeg
2 cups A.P. flour
2 tsp baking soda
1/2 tsp salt
4 cups raw, peeled, tart apples- diced or chopped small
1/2 cup chopped nuts
Cream sugar and shortening, then add beaten eggs. Sift all dry ingredients together, then add to wet mixture. Add apples last, then pour into a greased 9 x 13 pan and bake @350 degrees for 40-45 minutes.
Some of these recipes used the same amount of vegetable oil instead of shortening. Some also frost this cake, but I don't think it's necessary. Your recipe is pretty similar, but half size. Hope this helps.
ETA:I just noticed that your recipe uses the same amount of butter for the
8" x 8" size as mine (shortening) does for the 9" x 13".
Q