I'm guessing the new chunky boi cable may have substantially better / lower-resistance shielding, which is usually beneficial with unbalanced connections. The offending whine may have been part of power supply mains filter leakage current from the speakers making its way back to the computer via the audio cable. Then the amplitude of interference is pretty much going to be directly proportional to shielding resistance. A piece of bare wire touching both the computer chassis (or exposed grounds) and e.g. RCA sleeves on the speaker should have much the same effect when used with the old cable, assuming good contact on both ends.
An unbalanced audio input only knows about the voltage difference between signal and ground. If for some reason there is additional current running over the shield that is generating a voltage drop according to Ohm's Law, that voltage cannot be distinguished from an actual signal coming from the source. Typical floating SMPS have 1-4.7 nF of coupling capacitance to mains, which effectively forms a complex voltage divider with shield resistance if the computer on the USB is grounded.
Even if the computer should be floating, good shielding would be beneficial - if your system's ground potential is floating, you could have capacitive coupling from your signal wires to the outside world, like the literal ground they are on. Good shielding forms an effective Faraday cage and as such prevents the signal from "seeing" anything outside. This is particularly important if the output is turned off and impedance on the signal wires is limited only by speaker input impedance, which could mean 10 kOhms or more instead of a few ohms. It's about the difference between trying to move a pack of melamin sponge (magic eraser) or cotton wool vs. a same-size block of solid steel or lead (and actually, it could be as much as the difference between solid air and solid lead). This is why passive speakers are using nothing more than twin lead for wiring, any external capacitive coupling has to fight a fraction of an ohm of output impedance and speakers aren't exactly sensitive (you'd typically need about 0.4 mV just for 10 dB SPL at 1 m).
BTW, it's funny how the electronics are the smallest thing in the entire setup, being dwarfed even by the cable...