Can someone explain to me why I need more than an unmanaged switch to host an offline lan game?

I was wondering if someone can educate me as to why this didn't work.

I've hosted lan parties for years now, but this year I have a challenge to host one offline.

I thought it would be as simple as hooking up an unmanaged switch to all the computers, but I was having trouble finding the hosted game.

The two computers saw each other on the network(saw the computer name), but unable to see the lan game.

The lan game would actually recognize the IP and attempt to connect, but the error would be along the lines of "this game only allows users on the local area network to connect". Trying a random incorrect IP would give a different error like "unable to connect".

I noticed that their IP's started with 169.254.xx.xx and that was a symptom of no DHCP?

I've always had a router and modem connected to the switch, but I'm imagining that the unmanaged switch is a telephone switch board and the "router" is the person pulling the cables around and plugging them back in. Is that the case?