Hi:
It doesn't matter what operating system you are running, as long as you flash the BIOS using one of the DOS based flash methods listed in the instruction page that opens when you first run the BIOS file you downloaded.
I use the F10 Flash method that is listed on the instruction page. You will need a USB flash drive formatted with the FAT32 file system, and you copy the contents of the DOS Flash folder to the flash drive.
With the flash drive plugged into the PC, restart it, tap the F10 key, on the File menu, there is a Flash System ROM command. Select that, and follow the on screen instructions to update the BIOS.