Several things stand out in this genealogy.
Moses comes from elsewhere (Midian), but he is not a stranger; he is an Israelite. Exodus 6:15–17 connect with Genesis 46:9–10, where the sons of Jacob, along with their sons, are mentioned. Only Reuben, Simeon, and Levi are mentioned, not the other tribes, so it is clear that Levi (and so also Moses) belongs in the line of Israel.
The leader of the people does not come from the tribe of the oldest son of Jacob (Reuben), but from the tribe of the third son, Levi. More than once we read in Genesis that not the firstborn son is chosen by God as leader of the family, but another son (Isaac, Jacob, Joseph). Here that happens also, as Moses comes from Levi and Moses is younger than his brother Aaron (see Exodus 7:7).
The focus of the genealogy is on the line of Levi–Kohath–Amram–Aaron– Eleazar. With those names, also the ages and/or their spouses are mentioned, not with others.
The names are selective: Moses’ wife and children are not mentioned. Also, Miriam is not mentioned; we only learn her name in Exodus 15:20.
In Genesis, Abraham has a family in the midst of other families and nations. In Exodus, the emphasis is on Israel as God’s people, set apart from other nations. We do not read, here, genealogies of other nations or persons, and none of the nations’ forefathers is mentioned, not of the Pharaoh, and not even of Reuel, Moses’ father-in-law, a priest of God.
14 These are the heads of their fathers’ houses: the sons of Reuben, the firstborn of Israel: Hanoch, Pallu, Hezron, and Carmi; these are the clans of Reuben.