It says the player only chooses a new player to control Gollum, if able.
The player is not able to choose a new controller for Gollum due to the active location, so Gollum doesn't change control.
Yes - it's also worth noting this, from the FAQ:
(1.14) The word “cannot”
If a card effect uses the word “cannot”, then it is an
absolute: that effect cannot be overridden by other