Paging /u/snickeringshadow
This is an extremely difficult question to answer because of the sparsity of archaeological research in the area. The ball game was played in Michoacan, but the extent of it's popularity is still kind of up in the air. The only site that we know of which had a ball court used during the Late Postclassic (Tarascan-era) is at the site of Ihuatzio. In fact, Ihuatzio was originally called Querétaro which in P'urepecha' means "Place of the Ball Court." Ihuatzio was also a major religious center in the empire, and it appears to have been the one and only location in the Lake Pátzcuaro Basin where we can be sure the game was played in the decades leading up to Spanish contact.
However, the site of Angamuco (which is a provisional name - we don't know what the site was actually called) also has a ballcourt. Angamuco has a long occupation ranging from several centuries before the empire (carbon dates pending) up through the early colonial period. It has a couple of ballcourts, but we don't yet know whether they were used during the Late Postclassic or not. Angamuco is also located just outside the Lake Pátzcuaro Basin, between the lake and modern-day Morelia.
So this leaves us with one of two possibilities:
The ballgame was popular in the centuries leading up to the formation of the Tarascan Empire, but became less widespread following the rise of the empire and was restricted to state-approved ceremonial areas like Ihuatzio, or;
The ballgame was popular during the empire as well, but only one ball court was used for the Lake Basin proper. Other sites outside of the Lake Basin had ball courts.
In order to narrow down those possibilities we'd have to date the ballcourts at Angamuco and conduct much more extensive archaeological work in the highland areas adjacent to Lake Pátzcuaro. Since that hasn't been done we can't be sure one way or the other.
In either case, the ball game was played but seems to have been somewhat less prominent compared to other Mesoamerican cultures dominant at the time.