I have the exact same keyboard but rebranded by Anker. Yes it works fine over normal bluetooth with the Gigabyte H77N-WiFi MoBo. You just have to pair it like any Bluetooth device. The touchpad works but is very small and not as responsive as the touchpad on the Logitech K400 which I have switched to. I also like the larger size keyboard of the Logitech unit.
The only problem with the Bluetooth unit is that it will not wake up a HTPC from sleep mode since the Bluetooth receiver is turned off by default when the unit snoozes. I think you can configure it not to do so but I didn't bother because I preferred the larger keyboard.