You have a fair amount of high frequency buzz there (as opposed to hum).
That's going to be audible when the gate is open, any gate, regardless of how tight and/or tailored to your use it is.
You're also going to hear it cut off when the gate closes, which may accentuate it even more than not using a gate at all.
Best solution is to reduce the original interference, if you can, with shielding, good cables, clean power, moving away from computer and monitor, all the angles you know.
Gates aren't miraculous. They just shut down when they think there's no more signal, with both the detector and the attenuator parts potentially having different time constants and possibly frequency responses, possibly dynamically according to the signal. But they can't actually reduce the interference without affecting the signal at all.