This is the musical equivalent of a Title Drop; when the Title Screen theme for a game is played in a certain context within the game itself. This tends to lend significance to these scenes in a fashion similar to that of a Title Drop.
When the theme in question is a remix or re-used melody, this trope overlaps with Leitmotif or Recurring Riff.
Also compare Theme Tune Cameo, where the tune makes [...] [tvtropes.org]