Is it permissible for me to listen to an Islamic radio station that broadcasts songs with musical rhythms, while lowering the volume when these songs are broadcast, following a fatwa by Sheikh Ibn Uthaymeen regarding electronic games?

It is not obligatory to stop listening to the radio completely. Rather, it is sufficient to avoid listening to forbidden things, and to benefit from what is good and avoid what is evil, if possible. To strengthen faith and make good use of free time, there are previous fatwas that can be consulted.