The passage quoted in the question says that Nimrod's territory was in Shinar. We see Shinar again in the next chapter:
2 And it came to pass, as they journeyed east, that they found a plain in the land of Shinar; and they dwelt there.
3 And they said one to another: 'Come, let us make brick, and burn them thoroughly.' And they had brick for stone, and slime had they for mortar.
4 And they said: 'Come, let us build us a city, and a tower, with its top in heaven, and let us make us a name; lest we be scattered abroad upon the face of the whole earth.'
The people dwelling in Shinar are the ones who built the tower of Bavel, resulting in the disruption of language and the scattering of people throughout the world. It does not surprise me that their leader gets a little extra "air time" to describe him and his territory.
Genesis 11 does not actually name Nimrod as the leader of the tower project. Rashi points out the connection (on 10:8):
he began to be a mighty man: to cause the entire world to rebel against the Holy One, blessed be He, with the plan of the Generation of the Dispersion. — [from Eruv. 53a, Chul. 89a]
Eruvin 53a is pretty much what Rashi quotes. Chullin 89a, discussing the greatness that God bestowed on certain people, says (Soncino translation):
The Holy One, blessed be He, said to Israel, I love you because even when I bestow greatness upon you, you humble yourselves before me. I bestowed greatness upon Abraham, yet he said to Me, I am but dust and ashes; Upon Moses and Aaron, yet they said: And we are nothing; upon David, yet he said: But I am a worm and no man. But with the heathens it is not so. I bestowed greatness upon Nimrod, and he said: Come, let us build us a city; upon Pharaoh, and he said: Who is the Lord? Upon Sennacherib, and he said: Who are they among all the gods of the countries? upon Nebuchadnezzar, and he said: I will ascend above the heights of the clouds; upon Hiram king of Tyre, and he said: I sit in the seat of God, in the heart of the seas.
Please note: This answer was written for a neutral, academic audience
and is not intended to be interpreted in the context of a religious
belief or doctrine.