That Reddit thread seems to think it's spurious vibrations through the floor while doing it's job. OP stated that it's audible when the input is quiet or even silent, so this does not seem related.
Short of the long here, if the rumble is present and at the same volume no matter what the Wiim or sub volume is set to, then it almost has to be an issue with the sub itself.
Does it rumble with nothing connected? What about an alternate source input?
I'd think maybe a ground loop problem, but you only have 2 prongs. I wonder if it could be grounded though somehow and if that would help.. But even then, you'd more expect a 50hz hum opposed to a "rumble" if it were a grounding issue of some kind. I could be wrong though.
While I really don't think the Wiim is at fault here, I'm also curious if you have the ability and know-how to capture the analog output of the Wiim and analyze if there are spurious low frequencies. You could also test the output from the sub to see if it's adding that rumble within the audio chain. (I did tests like this when I was having some sub issues and was able to prove the Wiim was fine and the issue was indeed my sub.)