No, you can pass the controller states and timestamps to whichever node is acting as its server. You then extrapolate everywhere else until a correction arrives from the server. It worked magnificently and we used to watch efficiency improve up to 4 consoles and then gradually decline due to increasing latency. Never patented any of this, have at it, we have scads of prior art if anyone tries to do so :-)...

In this day and age, I suspect the latency issues would be unnoticeable on a 10 Mb/s or better router (which is to say any LAN party) but this was done in the mid-90s.