Running the linux binary update file looked good and it asked me to reboot. After reboot the same old v2.1.15 BIOS was there, not the latest v6.4.0 (as of writing this small post).
Next up was creating a FreeDOS Bootable ISO with the bios update program included (see this page for how to do that in Windows). Running the BIOS upgrade program from FreeDOS (virtual media and DRAC) I got this error:
Cannot use a "Dell System PowerEdge R710" BIOS in a " - "
Pres any key to exit.
ROM update not performed.
After some googleing I found the solution on Dell Community Forum - use the /FORCETYPE option.
So to force the update, I just ran the update package with that option (I had renamed the file for 8.3 DOS filename):
And thats it. v6.4.0 BIOS up and running :)