Unless I'm overlooking something, the demo only requires DOSBox to have a machine with predefined execution speed. There are no DOS interrupt calls that I can see. Other than that, the program could probably even be trivially modified to fit in a floppy disk MBR and could potentially run without underlying OS.
To be more exact (in an excessive way), it uses the BIOS's code to set the video mode (INT 10h) which is probably a few dozen bytes (at least?) although I have been remiss at not ever reading them. And it depends on DOS configuring the memory space to leave an INT 20h call (to terminate the program) at a place that's easy to RET to. But, yeah, very little extra. But I'm not being negative at all and this is pretty nice code and on the impressive side of 256 byte demos from the 80s and 90s (and onward).
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Thanks :)
and yes, your observations are spot on.
256 bytes (plus X kB of BIOS) (plus Y kB of hardware schematics)