What goes in a student success statement for a faculty application?
I would recommend e-mailing a contact in the department and asking them. I expect that the answer would be "It's just a teaching statement", although it could be different.

Another thing you might do is search the university's website for "Student Success" and try to get a sense of what particularly the university means by this buzzword. Keep in mind that this requirement was possibly imposed by higher administration, and the people reading and evaluating your application might or might not have high regard for the intent behind it.

Edit: (too late for OP, but perhaps still of interest) From what I can tell, when universities talk about "student success" they are usually talking about efforts to make sure that students don't fall through the cracks. So in a "student success statement" you might talk about how you've gone out of your way to help students who are struggling.