Preheat oven to 350 degrees F (175 degrees C). Grease 2 round cake pans.

Mix cake mix, 1 1/2 cups eggnog, eggs, butter, nutmeg, and 1/2 teaspoon rum-flavored extract together in a bowl using an electric mixer until batter is smooth, about 4 minutes. Pour batter into the prepared pans.

Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 30 minutes. Remove cakes from pans and cool on a wire rack.

Mix 2 cups eggnog, vanilla pudding mix, and 1/2 teaspoon rum-flavored extract together in a bowl until smooth; refrigerate until pudding thickens, at least 30 minutes.

Mix cold water and gelatin together in a bowl until gelatin is dissolved. Beat cream in a separate bowl using an electric mixer until soft peaks form; add gelatin mixture, white sugar, 1/2 teaspoon rum-flavored extract, and salt and beat until stiff peaks form. Refrigerate topping until chilled, at least 30 minutes.

Place 1 cake on a serving plate and spread 1/2 of the filling on top. Place the second cake over the filling and top with remaining filling. Cover entire cake with whipped cream topping. Store cake in refrigerator.