As an example, here is the original iconic melodic phrase that's used throughout the Trails Sky games:

https://youtube.com/embed/3GB-xej4GFc?start=66&end=85

But here in this next piece, the exact same melody is used with a more upbeat "jazzy" rhythm (certain notes are shortened and pauses are inserted):

https://youtube.com/embed/cY_WTw4_rEA?start=50&end=80

Is there a name for this general technique? Or is there a name for the particular "jazzifying" done in this example?