I was using a 486SX with DOS 6.22. I'm just using a renamed copy of the dos folder included in the download copied to the c drives. I've since tried it on a PII with the same setup and get the same bug. So I tried a fresh download on DOSBox and I still get the same bug every time when I try to put the statuette in the panel. As far as I can see it's nothing to do with hardware and happens every single time without fail so it should be easy to reproduce. I didn't have the same issues on a CPC I'm glad to report.
There was another very minor issue on real DOS hardware in that the batch file doesn't work to launch the game. It looks like it's breaking the first line up into two parts when trying to run it. Opening it with edit, it looks normal enough. I removed the carriage return after the first line, put it back, saved again and it was fine. Maybe just opening and saving would have done the trick? Not sure what the issue is there - it works in DOSBox. I thought that maybe it's using some unsupported text encoding format but that's speculation.