No. Copyright fees are included in the 1078 yen monthly fee, so you can play music all you want.

The music on BGMC Station is entirely original, produced, and performed by BGMC Records.
We do not outsource the management of the music to copyright management organizations for playback in shops, and we do not receive any copyright fees from copyright organizations for playback in shops.

In other words, we own and manage the copyrights for playback in shops, so there is no need to pay the copyright management organization.