While the app requires a certain version of Android, the audio tour files
themselves are generic .mp3 files, and are not dependent on any version
of the Rick Steves app to be played. You can use any music player to play
the files.
I believe that what the app gives you is a nice organized interface to regions
and tours, but it is not the end of the world if you download the mp3 files by
themselves and rename to be indicative of what the content is. It certainly
beats spending money on a new phone just to be able to listen to audio tours,
which are more or less a verbal version of what's in the guidebooks.
But, if your phone is using an older (say, Android 11 or earlier) version, then you
need to upgrade anyways, as your phone is probably no longer getting OS
updates and you are at risk for security issues, etc.