I'm not sure why, but the two hackers fighting to get control of a tv station's tape robot is simultaneously the greatest and most ridiculous thing in that whole movie.
Even that is sort of sensible, actually. Just not in the exact manner depicted.
In say, an Unix system, a tape robot is going to be hooked up to some sort of SCSI device, and probably nothing prevents two people from commanding it at once in conflicting ways.
Two people logged into the same system trying to figure out who the other one is and kill their login process or to disable whatever way the other guy used to get in -- also possible.
Even two people typing at each other is a thing. Linux has the 'write' and 'wall' commands, and there even was a realtime chat program:
So yes, the entire scenario of two people breaking into the same computer, sending conflicting commands to the tape robot, trying to kick the other one out, and even sending chat messages at each other is very much something that's plausible on an Unix system. Just without the colorful graphics.
https://youtu.be/2efhrCxI4J0