Ugh. It's not by default "illegal", unless it provably violates Part 15.
Has a Part 15 assessment been done yet? Have we analyzed power emission levels to assert that this thing is indeed 'breaking the law'?
Has this device been checked by the FCC for spurious emissions during normal operation? Did it pass, or is it chinese jank uncertifiable garbage?
Edit: C'mon downvoters. If you make a claim that it's "Illegal", you need to have some sort of proof that its the case. And I'm not immediately seeing it. Further research? Sure.
This is mostly correct, except for FCC exceptions for stuff you build yourself. For example, it is legal to broadcast on the FM band if your signal meets certain signal strength criteria. Also, the FCC itself doesn't do assessments, they are done by independent (expensive) labs.
The wire is being used as an antenna. When you use UART, you have the other end of the wire terminated with another circuit. (i.e. The energy goes to into the connecting circuit.)
Because the wire ends at an open circuit, the currents on the wire radiate, turning the wire into an antenna.
Wires connected to a closed circuit will radiate too, if you drive them at high frequency. Maybe not efficiently, but it'll still radiate. There's nothing special about an open circuit that makes an antenna work.
Shielding (e.g. coax, or a properly grounded enclosure) is what prevents ordinary wires from becoming antennas.
Normal rs232 is run through shielded cables as well. It was standard practice to wire the d-sub connectors to the cable shields. The wires themselves may not have been shielded, but the cable was shielded against being an antenna.