Arduino #1 on one computer would have to be connected to Arduino #2 on the other computer and digital I/O communication would have to be added to each Arduino code. I would try to use the smallest micro controller possible.
This is a simple outline.
Computer #1
int pinA = 3;
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pinMode(pinA,OUTPUT);
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digitalWrite(pinA,High);
trigger device
Computer #2
int pinB = 4
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pinMode(pinB,INPUT);
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val = digitalRead(pinB);
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if (val >0)
{
trigger device}
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