This is “Virbank City” from “Pokémon Black2/White2”, developed by Game Freak, released by The Pokémon Company.
This is composed by Hitomi Sato.
This music is played when you arrived at a port city named “Virbank City”, where the second Gym is located.
The Unova region is based on the United States (New York), so “Virbank” is probably a reference to “Burbank” city in California.
The impression of jazz is probably due to the use of tetrad and chords that contain tension such as 9th, 11th, and 13th.
The first half of the song (part A) is mostly iv-V-i.
From the 9th bar, notes outside the key are used so the impression changes a little.
I couldn’t analyze around here, so please consider the chord degrees described in the score as just a note.
The second half of the song (part B, 0:34~) uses IV-V-I of the relative keys and iiø-V-i.
It’s a chord progression that is smooth, straightforward, and comfortable to listen to.