Domicile can be anything but it has to be a space that someone resides in on a semi permanent basis. One of my OCs, Kate Labelle, was at a boarding school over the holiday. She took half the dormitory with her into the Medium. It's possible that it took half the building because by that point, with a looming apocalypse, she had started breaking into other dorms. Thus she saw the whole building as hers rather than just her own room. If there were other people in the dorm who knows what would've happened.
And a game can start with no players if no one involved in starting the game qualifies (between the ages of 13 and 18, or local species equivalent). A bunch of government scientists running the program on a mainframe without a distinction between server or client, also having modified the game to reduce it solely to its worldbuilding aspects, would have no players.
And yeah. It just snatches random people who qualify! You’ve never even heard of Sburb and suddenly you're master of a Stronghold and partnered with another player you’ve never met but who has their own stronghold. It got pretty fucked up in the RED KING session! (As yet unwritten)
If you're interested in the series, this is worldbuilding background for Sburb². I'll probably end up writing out the RED KING session eventually as a part of this: https://archiveofourown.org/series/4994056