As far as I know the music is higher quality, but that is not the point; I was wondering if maybe it made things easier for you writing the script for the game. Wine is still being actively developed, and while it does probably take more work to try out different versions of Wine you do have more choices so I think you could make the game run better and have less work to do maintaining the script for when linux distros update.
Even if it does not look like it, DOSBox is still actively developed ;)
But I might add support for the Windows installer in the next planned update for the script.
Let’s go back to your issue: I managed to reproduce it by installing the 64-bit version of DOSBox provided by Debian Stretch, and switching to the 32-bit version seems to fix it.
You can do this by running the following command as root:
apt install dosbox:i386
Please try this and tell me if it fixes the issue for you.