It is hard for me to believe that uchicago.edu should outrank illinois.edu. Illinois.edu is a famous top-tier CS program; uchicago.edu is a top-tier university with a relatively small CS program.
Regarding undergraduate and masters' education, U Chicago degrees have top-tier status despite much lower selectivity than comparable schools, so maybe that attitude is worth something.
(I studied electrical engineering there and as much as I hate to admit, because I wasn't motivated enough to seek out attainment of more industry-ready skills, it actually set me back significantly as an engineer)
I don't think Chicago Theory > UIUC Theory seems absurd. Certainly not like Penn > CMU.
I think many CS programs are, or should be, how to engineer software. Of course, any engineer must study the science behind the field.