The technical aspects have already been considered: the local network will be on Wi-Fi. If someone doesn't have Wi-Fi on their laptop, we'll connect them with a cable. I have the cable, and Jackie bought the connectors. The only thing is, if anyone has a crimping tool, please bring it just in case. I've arranged it with a friend, but if something goes wrong, it'll be a problem.
Tvarina's computer will be used as the server, and the stream will be on his channel. The plan is to capture the image from the computers on the local network, and Tvarina will process it and send it to the internet. I'm not very good at this, so I'm asking for help from experienced streamers on how to organize the image transmission over the local network using your favorite programs. The methods suggested above are not an option: I know the person who offers remote admin access, and the second program, judging by the description, has similar functions. The essence of both is remote control (i.e., interception), so players won't be able to play properly. Those who are familiar with XSplit, please look into it to see if it can be connected to the local network. Otherwise, we'll have to use the TV, as I saw that function there.
At the same time, the stream will be broadcast on a plasma screen. The second plasma screen is still a question: we can display the stream from the internet (or watch recordings) on it, but it's located close to where the players will be, so they might hear the commentary and accidentally see the image. We'll decide on this on the spot. Another idea is to start a stream of the overall image from the room, probably on my channel (snooppy_hw on Twitch), so follow the thread. Both of these options are possible if we have "extra" laptops, so bring everything you can.