USNWR rankings are based on a number of things but two really matter: 1) Overall NIH funding to the institution 2) "Prestige ranking" of the institution. From the start a high prestige ranking was assigned to Harvard, Stanford, Hopkins, NW, etc. and it is very difficult for institutions to move up the list. Match success and USMLE scores do not factor into the rankings I believe (and if they do, very small part of them).
UIC attracts a good number of very good medical school applicants from IL and the Chicagoland area. The top 10-15% of the class could give NW or UChicago a run for their money USMLE score wise, intelligence-wise, etc. Additionally, match is both a numbers game and a networking game. You have to hit your scores but who you know also matters. You have a lot of daughters and sons of physicians there, providing their kids a boost once they are ready for match. Plus, UIC has a very strong alumni network in Chicago and the mid-west. Also, UIC graduates ~300 MDs a year, resulting in more of them eventually reaching decision-making positions in academic residency programs and providing a boost to future UIC residency applicants. All in all, this creates an institution that "punches above its weight" as you put it.
TL;DR: I would focus less on USNWR rankings and more on USMLE scores (especially looking at top and bottom quartiles), match results, rotation quality and location, and student resources when looking at schools.