Alright, HP has helpfully provided two probably almost identical graphics drivers ("AMD High-Definition Graphics Driver") and chosen not to specify which one should be used. But the first of the two listed, the one posted on January 16, 2018, supports all the graphics chips that the second one does and a couple more, so that's the one to try first.
When running the driver, right-click on the installer and select "Run as administrator." If you get an error, restart your computer and try the driver from January 11, 2018 instead. If you still get an error, please let me know what it says.
If you do get the driver installed, restart your computer, then check the Device Manager to see what's listed under Display Adapters, and if you still see the Basic Display Driver, please post another dxdiag.