Yeah, that was the game. MIDI Maze was great fun in multiplayer, and as you say a very early networked death match game, far before any iD game existed.
The funny thing is that because the machines were networked in the shop we played it in I never knew how the actual network was setup, until just now when I read that wiki page! The game title now finally makes sense. Quite a unique idea to network machines using the midi ports.
And I agree about those ports too. It was completely stupid sticking the joystick ports under the ST so you had to lift the whole thing up to get to them. Most people ended up with joystick extenders so they didn't need to do that.
The Falcon was definitely a great idea. Basically just an updated ST, much like the A1200 compared to the A500. But as you say, it came too late to save the ST from demise and wasn't marketed or sold properly. Whispers: "I had wanted one too."