The first thing to point out is that this is a ballad and there are no improvised solos on this song, just the melody once through, then back to the bridge to the end. So the only improvisation comes in the form of embellishing and filling around the melody. A ballad is not a “style” simply a type of song.
Another thing to point out is that Oscar Peterson transcended “style” throughout his career. He was equally adept at playing stride piano, boogie woogie, block chord melodies and harmonies, swing, blues, bebop, hard bop, and lyrical ballads like this one to name a few.
I would say as far as piano styles for this song go Oscar is basically incorporating 2-3 different stylistic elements of jazz piano. One is playing right hand melody with left hand rootless voicings (leaving the roots to the bassist) the way pianists did in the bebop era and beyond. Another is embellishing and filling around the melody reminiscent of Art Tatum. The third is playing block chord harmony under his melodies in spots. All of these elements make up some of the parts of the standard vocabulary of jazz piano.