Looks more like bad design unless there’s a ton of other cables or if some of your cords/cables are in loops. I just checked my amp/preamp, and surprisingly they’re not using grounded plugs either, and it’s fairly high-end gear.

Only other thoughts:

• plugging directly into the wall if you’re plugged into a surge protector, or plugging into a Surge protector if you are plugged into the wall.
• I would also try moving the volume up and down a little bit because I’ve seen gear where that caused hum issues (god knows why).
• try plugging in a source in case they’re somehow using the connectivity to other gear to provide the grounding (grasping at straws here).

Unfortunately, it’s been long enough since I’ve dealt with ground hum issues that the I’ve forgotten all the tricks. :( You might need to find an audiophile group. Because even cheap-ass gear shouldn’t do that.