"Er trinkt während sie isst."
Yes, "während" is a genitive preposition, if it is translated to "while" or "over", and if a noun phrase/nominal phrase is following. E.g. "Er trinkt während des Spielens" = "He drinks during playing".
Während is a Genitiv preposition, but it is commonly used with Dativ by native Germans.
Während is not used as a preposition here so it does not govern a case at all. It is not "sie" because of "während but because of the grammatical function "sie" has in the second sentence-part. This example should be moved away because it has nothing to do with prepositions.