The band was officially identified
From The Lost Media Wiki
The band is called "Change To Win". The song is called "Just A Game" (shocking, I know ᕙ(͡°‿ ͡°)ᕗ), released in 1988 for charity event, according to info from vinyl that was saved by one of band members.
Quote from Christof Bachmeier: "I played the piano and the bass, Gigi „Angel“ Schleifer on Guitar, Wolfi Lohmeier on drums.
Mario Lehner, a close friend of mine and a great singer passed away in 2010, he is the man with the voice!
I sang the first part, the second part is Regina Simon, third part is Karli Mayer."
https://www.reddit.com/r/NowIKnowItsJustAGame/comments/1dtn67r/just_a_game_solve_megathread/
The game is over!