So... I noticed a little something after a while, I'm not sure if anyone here is aware of it as, once again, it isn't explained in the game or elsewhere.
The host of the match is chosen randomly. There is no clear indicator of who has been chosen, but it is extremely likely that this person will be the only one with a four-bar connection strength (the host's connection strength will never be less than four, the max). The host will experience practically no lag, giving them a slight advantage. If this person quits or is disconnected, the current game will end, with the message "Host ended game."