Even if the feathers may not solve a physical purpose, There could be some reasons for their existence like:
A peacock has those bright beautiful feathers as a tail, they don't serve much of a purpose other than the real purpose, that is attracting a female. Almost all birds use their feathers to attract a potential mate. Your creature may use these feathers to attract females, additionally, if the feathers can rise at the creatures will it will add to its beauty.
Just like any animal's instinct, if you can make yourself look bigger, you can easily threaten others, including predators, enemies of the same or different species.
Estimate age and health
Though it may seem absurd and useless, the color and/or size of its feather can show what is the individual's state of health and relative age. A young can have pale feathers, an adult will have bright colors and an old will have faded colors. similarly in case of health.
Just had a very exciting idea, what if the female lays the eggs, on the feathers of the male, making it a sort of nest, and even after hatching the babies stick to the feathers.
The movements of these feathers may act as a possible medium of communication between these creatures, not too complex like a Morse code, but something better than a dog wagging its tail.