The game is based on the first versions of Mario, and your mission (how could it not be) is to advance from screen to screen until you release the princess.
South Park Super Mario Bros maintains the stages and the original theme of Mario Bros, even respecting the enemies and the levels. Nevertheless, there is no other innovation than its main characters, so if Mario didn't interest you in its time, it will probably not interest you now either.
Jump on the mushrooms and turtles, avoid the carnivorous plants and get to the finish in the least possible time to gain more points. Do you remember how you used to do it?