I got things working, but I now see the pattern which causes the problem.
I managed to reproduce the problem again. So it goes as follows
The problem appears with games I had installed from CD-Images in magic dos box. The ones in question were Jagged Alliance : Deadly games and Daggerfall. The first time I just copied the games CD images to the phone SD card, then mounted them in Magic Dosbox and made the installation through MDB. In this case I got ‘Can’t open..’ problem that I was describing, even though the installation was a success and files copied.
Then I did the same on the PC. I have installed the game from the game CD, and then copied the already installed files to the phone sd card. In this case everything works fine.
Basically running the installation procedure directly from the cd image on the phone sd card causes the behavior I have initially described.