I tried "installing" the files manually, but the installer also doubles as a sound device configuration programme, and will not allow to configure sound and music unless the installation itself has been completed first.
The solution to this turned out to be quite simple. There is a file in the INSTALL folder of the demo distribution which is called INSTALL.INI. Essentially, it's a script for the installer programme. And it turns out that one of the lines that should display a progress bar during the installation was commended out, and DOSBox fails to interpret the script properly because of that.
So to fix this issue and install the demo in DOSBox, you just need to open INSTALL.INI in a text editor and find the line which begins with
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;English=