Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Combine cake mix, cherry pie filling, eggs, and oil in a large bowl with an electric mixer on low speed until moistened, about 30 seconds. Beat at medium speed until a light and fluffy batter forms, about 2 minutes. Pour batter into prepared baking dish.
Bake in preheated oven until a toothpick inserted into the center comes out clean, 26 to 30 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.
Heat sugar, butter, and milk together in a saucepan over medium heat. Simmer, stirring constantly, until smooth and thickened, about 5 minutes. Remove from heat, add chocolate chips, and stir until dissolved. Set aside to cool and thicken to icing consistency, about 20 minutes.
Poke holes in top of cake. Pour chocolate icing over cake, allowing it to run down edges of cake.