I've noticed this is different per game. And I believe, based on how the system seems to work, that there is essentially a dedicated music channel (separate from like a sound fx channel). Some games have an option for me to turn of the in-game music with a different toggle for in-game sound fx. And on those games, if I toggle off their music, my own music will continue playing without interruption; the sound fx from the game play on top just fine. But when the game's music toggle is left enabled, starting the game ends any music I had playing, even if the game doesn't yet have its own music started.
What's more annoying is ads on webpages that have sound aimed at that music channel. Nothing is more obnoxious than my music being stopped because a web ad took over the channel.