Well, the list of chipset change very often and it' not easy to keep up with them and all the different drivers that exist. So, a chipset that isn't marked as supported can work. Do the injection test.
So, I'll assume that's the manufacturer driver and in this case, it doesn't support monitor mode. Or you can try the injection test to see by yourself. And try wlan1 too.
You'll have to kill them or you'll have issues with other tools (including testing injection).