The source material is that a new york plumber is travelling through a psychedelic fantasy landscape to rescue a princess from a tyrannical dragon turtle.
I love the 1993 mario movie, I think you really summed up why I was so forgiving of the liberties it took. As a kid I had superimposed my imagination on the very limited source material and the movie just did that in a direction I didn't expect.
I have also heard that in its development there were the designs of a much darker cyberpunk world which was ultimately vetoed somewhere up the ladder, that sort of explains some of the weird choices.