The ATC operator chooses a command from a UI: 'JAL 123' > 'Runway 34R' > 'Clear for landing'.
Everything cascades automatically from there: ATC's on-screen maps and info, airport lights, commands to all relevant planes (including 'Runway 34R' > 'Hold short').
Transmission to planes could be digital. Given the relatively few possible commands, we're talking very little bandwidth, plenty of room to ensure error correction, redundancy, etc. - and perfectly accurate reception.
All planes would show the exact command on a screen, their maps etc would update, and they could play locally generated audio of the command.
I know nothing about aviation. (I do know that entirely rebuilding matured, critical systems for the new technology is rarely a good idea - the trick is to start with one small subsystem, work out the bugs, mature it, and grow from there.)