I may be on to something here... the PC I'm trying to connect to does not have it's own Bluetooth interface so perhaps that's why it's not seeing the mouse. I had thought the guide was referring to using the dongle as the connection point, but now I suspect the dongle may not be capable of being that, and that the guide is really showing a connection to a non-Cypress interface.
Am I on the right track here? Is it possible to make the dongle work in that way?
Yes, the assumption is correct. The example will work only if the Host supports BLE inbuilt. In case of Windows, you can test with Windows 8 or later versions.The Windows 7 and older version does not have HOGP drivers.
Please refer to the BLE_HID_Keyboard example project datasheet section "Project Description".