The board that you liked doesn’t look like the one discussed earlier.
Looking at the board in the listing you linked I don’t see anything that would handle conversion from logic levels to RS-232, just an old UART chip and a few accompanying 5V logic level ICs. There are also no obvious connections for +/-12V that would normally be required for RS-232 without voltage pumps. The typos-filled note on the page mentions RS-232 but in this case I would first try logic levels.
This module is designe according to Kenwood documentation and will work wioth RS232 cable connected to your PC!