The FT232H you linked in the default UART configuration has no GPIO pins according to the datasheet pin description table. You need to change to MPSSE mode or similar using the flashing tool.
The Adafruit FT232H works out of the box with pyftdi and libftdi. You don't have to use any special tools or flash it in any way. The USB commands are handled by the underlying libraries.
https://www.adafruit.com/product/2264 - USB to GPIO (and other stuff)
"Bus Pirate"
Or get a RasPi - it's not your desktop PC, but they're running Linux with direct GPIO access available in userspace.