No one should run a local subnet on that range as it's super-easy for an attacker to get in on it and is usually a sign of a lazy network admin.
Hosts files? It's a lot easier to run a fairly secure mini-DNS system on your local subnet that would make things a lot easier.
Internet \--> (public IP) cable modem (192.168.1.x) \---> Router (169.254.1.x) \---> Machine 1 (169.254.1.11) \---> Machine 2 (169.254.1.12) \---> Machine 3 (169.254.1.13)