We don't know exactly how the weapon works, but consider it is not a normal computer virus (which could potentially be distributed through the comm systems) but an actual physical thing that was in close proximity to the relay station when it attacked. It's quite possible it doesn't merely upload a virus into the target's computer, but that the construct actively works to suppress defenses and to spread malfunctions and worse everywhere. In other words, it may be necessary for the construct to be present in a certain range in order to have the desired effect.
An infected system could potentially try to send a virus through long range communication, but whatever firewalls and other antivirus measures Starfleet has could possibly stop those before they can do damage, without the construct there to do its thing.
