I finally got around to testing this out, and it isn't working correctly for me.
I granted the new "Move threads" role permission for this to social group admins and moderators. I then tested within a group which has 2 discussion forums, each with a thread or two in it. I tested using a standard user account which does not have any special permissions in the overall forums, but which is set to admin role of this particular social group.
The "Move thread" option shows up, but the dialog for it does not list any forums available in the "Destination forums" list. And again, this test social group has 2 discussion forums within it, so at the least I would expect the other discussion forum of this group should be showing up as an option.
All users (including even someone not logged in) can view those forums, yes.
The whole section for Social Groups discussion forums was set to not show on the forum index, though they remained accessible. I even tested switching that back so that group discussion forums are all (except for private groups) even visible on the forum index. No difference, the destination forums list remains empty. I guess I should add that the group I tested within is a Public group as well, not a private one.
I also tried rebuilding the permission, forum, and thread caches in the admin panel, no change.
Anything else you can think of?
Perhaps it might work with a newly created group and newly created discussion forums, since this was an existing group and existing discussion forums from before I updated to the latest version of this addon? I'll try that.
Tried the above just to be sure: newly created public group, with 2 newly created discussion forums in it, and a new thread created in one of them. Same problem, empty "destination forums" list when trying to move the thread with regular account which is set to admin of the group.