Is Global domination rules just playing until one side controls all the territories? Any clarification would be appreciated.

In practice, a global domination variant is one where the sides ignore the official victory conditions, which are based on controlling a certain number of victory cities for a turn, and instead play until one side concedes.  You could play until all territories are controlled, but that outcome is usually determined well before the last enemy territory is captured.  Typically, experienced players can decide if a game is worth continuing after one of the major capitals falls.

As some have pointed out, this type of game can be less interesting because the Allies’ economic might encourages them to grind out a longer game until they can pour all their resources into crushing Germany or Japan.

Conversely, it presents a greater challenge for the Axis while also making the Allies less defensive as Cow mentioned.  The problem as I see it is that any game that lasts longer than 10 turns becomes a de facto Allied victory because of the economic imbalance.  Consequently, we’ve been trying to formulate a bid to help even things out, but not break the game in the first 3 turns.  It’s a bit of a round peg/square hole problem, but it’s good to get people talking about it for those of us who cling to the old “global domination” victory rule.