The bottom boxes are not connected or open to each other in any way. So, in the left stack there is a queen, and in the right stack there is a queen. The queens are 100% separated from each other. They cannot kill each other.
On top, in the middle, there is a queen excluder, so she cannot exit or cross over that way. On top of that are the honey supers.
As to why the workers don't fight, I don't know, but they don't.
Swarming is always possible, but the hive is huge, with lots of space, so I hope there will not be swarming pressure.
About the 2 queen hive, apparently that happens in nature sometimes, and maybe in our hives more than we know. I once saw 3 queens in a normal hive, and they did not swarm. Eventually only one queen remained.