Thrill of the Hunt

This card banishes a friendly unit and then allows to play it back to a battlefield as part of the same effect. The BF might temporarily be empty without loss of control.

CR 321: while a chain item is resolving, a cleanup can not occur.

CR 323.6: while the turn is not in an Open State, there is no loss of control.

The controller doesn’t lose control of the battlefield during the resolution and neither after since there is a pending unit on the Chain.

WHAT THAT MEANS During the resolution, the state is Closed. After the resolution, the unit is pending and the state is still Closed. The condition for losing control (CR 187.4.c) is never met, and as such, you’re allowed to play the unit at the BF you were controlling if you banished the only unit at that BF. This may happen both during a Showdown and in a non-Showdown scenario.