Ear-trained pianists who have taken music history lessons think in relative pitches (intervals). At least in the Royal Conservatory of Music history lessons I took, I learned about sonata-allegro and sonata-rondo form. Both forms involve sections and their transposed versions in the same piece, and in order for listeners to recognize the transposed versions, they need to think in terms of intervals.
Some video game soundtracks also encourage listeners to think in terms of intervals--for example, Mario Kart: Double Dash raises the keys of its racetrack themes by one semitone during the final lap, and UnderTale's soundtrack contains leitmotifs for several characters and then transposes those leitmotifs in different situations where those characters appear. In both cases, the transposed versions are expected to be recognizably similar to their originals.