In addition:
The problem is solved.
I had it with several games. In some cases there were problems with the lay-files (typing errors etc.)
However, in two cases everything was fine with the lay-files but I still had the problem that the game appeared on both screens.
When I opened the "video options"-menue it says "Marquee only", "Screen0 Standard" and "Screen0 Pixel Aspect". And then, in two out of 135 games I had to chose "Marquee only" manually and suddenly it also worked for the two games with that issue. I have no idea why this was different for two games while it worked for the rest.
However, maybe this further information is helpful for someone.
Best regards
Max