Headline says "online", but the description sounds like they're on the same LAN. This matters because the latency between the systems (LAN latency ~ 1ms, corresponding to frequency of ~1000 Hz) is faster than the phenomena they're measuring (2-45 Hz).

I'd assume the mechanism is that the player has a lot of physicality, so their brain's pretending the on-screen avatar is part of their body. If latency is artificially injected into the display or controls or both, do the brain waves develop a phase offset? Or does latency just cause the game's sense of physicality to break down?

Is interactivity and real-time interaction a necessary component of brain wave synchronization? Or does it show up in non-interactive settings as well? How could this be tested?

I'm thinking what might be going on here is the game forces players' brains' movement processing to physically simulate the same vehicle. The brains aren't syncing with each other, they're syncing with the on-screen object they're controlling -- which is the same for both players, causing their brains to sync -- transitively.

Simply put, if Alice's brain syncs with the vehicle on screen A and Bob's brain syncs with the vehicle on screen B and the two screens are in sync with each other because that's what the game's networking code is designed to do, the EEG ends up measuring Alice's and Bob's brains to be in sync.

I'd be interested in extending the experiment: Instead of giving the two players a real-time multiplayer game, have them play a single-player game one at a time, and see if their brains sync to the gameplay in the same way.

One problem is replicability. To produce the sync phenomenon, you might need a game where the controllable character with good "physicality" -- a tight feedback loop between its movement and inputs, to convince the player's brain to treat their on-screen character as an extension of their body. Give the player a character they can't control, and their brain isn't convinced the character is a part of them, and doesn't sync to it in the same way.

But if you give the player a character they can control, different people playing the game at different times will have different inputs, meaning the phenomenon could be there but you have no way to measure it. That is, Player A's and Player B's brain waves might sync to their individual games, but you can't measure that with similarity analysis anymore, because in Player A's game the vehicle took a different track than in Player B's game.

One way to solve this problem is to give them a character with a physicality they have to consider but can't control. For example, shooting targets from a vehicle -- your brain has to simulate the vehicle's path to aim your shots, but you can't control its movement directly. The players' brains' simulations of the vehicle might end up in sync, leading to their brain waves being in sync.

Another way to solve this problem is to create a game with little margin for departure from the correct path -- think about a Mario Maker speedrun level with a tight timer. Successful runs by different players will have very similar character paths and controller inputs, because significant departure from the optimal path results in failure. See if brain waves of different players may end up in sync as they're executing the same moves with the same timing.