The culture extended further than just the Mississipi. It's just the Mississipi river valley played a major role in the trade and communication which enabled the creation of the Hopewell tradition (mounds, raven motifs, pallisades, etc) from which Mississipian tradition (an evolution of Hopewellian traditions once large scale farming of maize is adopted, enabling larger cities and all that comes with them).That was going to be a given. They are called Mississippians because they all lived in the Mississippi River region, and were the ancestors to all the eventual tribes.
The full extent of it looked like this with many local subareas.

The subareas are more easily visible here:

Humankind's Mississipians as well as Civ 7's rendition of these people both draws upon the Cahokians of the Middle Mississipian complex.
But it really wasn't just people living along Mississipi.