Ground/Neutral is irrelevant here in order for current to flow there needs to be a potential difference.
In a regular 220/230/240v system you have a 240v RMS leg/conductor and a 0V leg/conductor naturally with a potential difference of 240V RMS. The fact that the 2nd leg/conductor is 0V doesn't matter, so long as it is different to the 1st leg/conductor current will flow.
In the 2 phase system you are still getting a potential difference of 240V RMS in regards to the 2 legs/conductors it's just that rather that one leg/conductor being at 0v it is at 120° out of phase with the 1st conductor, this means that when the 1st leg is at +120V RMS the 2nd leg is at -120V RMS creating the required potential difference of 240V RMS.
The tube network in London uses a DC version of the same sort of thing and also has no direct earth and trains designed for +750/630V - 0 work just fine on +210 - -420.