Making it in 1981 would have been a lot more difficult - we cross-compiled (or cross-assembled) most of it on modern hardware and the graphics conversions would have been very slow without a modern PC. Not to mention the modern tools used for composing the music and drawing the art, or how much we used the internet for research, or how we built on many years of demoscene research. But there's no theoretical reason why it couldn't have been done then.
The 'impossibilities' are mainly on the software side: we require DOS 2.x, which didn't exist yet in 1981 (although it will run on a 1981 machine). You would also need DOS 2.x to support the 360KB double-sided 5.25" floppies. They existed in 1981, but early DOS only supported 120KB per side, and early PCs were fitted with single-sided floppy drives.
But this could all be worked around (and some parts could be modified to require less memory as well), so all of the audiovisual effects you see in 8088 MPH are possible on an actual stock 1981 machine, with DOS 1.0 and a single-sided 5.25" floppy drive.