IL still has some counties with no detail.
For some reason, the Census Bureau did not release the data for MCDs in a few counties in IL and other states, while states like PA are completely released ...
Looking at the table I see the problem is that there are 16 counties that don't use townships, so they use precincts as their MCDs. The Census tabulated the population for 2010 and the table in the link has that population. However, the initial map references the 2013 estimates, which don't include precincts unless they coincide with places such as Valmeyer in Monroe county.
I found that clicking the date button at the top of the map toggles the data set so one can get everything for the state.