If you own the original GTA1 (with "gtados" folder) you can try it out in
dosbox. Note: Only the old CD version works. The re-released "Classic" version
doesn't have the DOS executables.

It takes ages to load the menu, even longer for the actual game and once
it starts rendering in all its VGA glory, the framerate hits rock bottom

I've come across an open source port, though: OpenGTA, Screenshots.
Maybe that could be ported?

Edit: It lists OpenGL and PhysicsFS (?) as requirements:
Maybe if software accelerated OpenGL were quick enough for GTA1,
it would make sense to port all those dependencies. Could someone
make an educated guess?