Appointing someone to rule over all that one owns denotes guardianship rather than an outright gift; Eliezer is the biblical example.
On the daf / in context: The verse is used to distinguish the language of appointment as steward from the language of absolute gift. Because Avraham later gave everything to Yitzchak, Eliezer’s “rule” could only have been fiduciary.
Type of Learning
Custom (halakhic inference — language of apotropos)
What Is Learned
Designating someone as “ruler over all that one has” creates a guardianship, not an outright gift; Eliezer’s status under Avraham is the Torah’s paradigm for that language.