I think this could actually be a feature. In a real game, the players self-enforce the turns, and when someone gets distracted and plays out of turn, it's hilarious to banter while setting things straight again. Of course that would need the videocall part.
A few years back there was this great platform for playing Magic: The Gathering, which didn't enforce anything at all and it was still great. Even did a few tournaments using it.
As long as all the moves are logged, you can enforce the rules by yelling at people.
Magic does have the problem that sometimes, in specific edge cases, players can disagree about what should happen based on the rules. It's hard to come to consensus via the yelling at people protocol.
Also, it doesn't enforce who's turn it is.