Measure the cereal into a large mixing bowl and set aside. Line a large baking sheet with parchment paper.
Combine the white chocolate chips and butter in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until completely melted and smooth (about 1.5 to 2 minutes total).
Stir the dry cake mix into the melted white chocolate mixture until well combined and no lumps remain.
Pour the white chocolate mixture over the cereal and gently fold with a spatula until every piece is evenly coated. Work quickly before the chocolate begins to set.
Add the powdered sugar to a gallon-sized zip-top bag. Transfer the coated cereal to the bag, seal it, and shake vigorously for 1-2 minutes until all pieces are covered in a snowy white coating.
Spread the mixture onto the prepared baking sheet in a single layer. Let it cool for 5 minutes at room temperature.
Sprinkle the rainbow sprinkles over the cooled puppy chow and gently toss to distribute evenly throughout.
Let the mixture sit for 10 more minutes to fully set before transferring to a serving bowl or storage container.
