I'm experiencing the same problem, but luckely found a workaround:
"Update failed for: LICENSE, Error: The system cannot move the file to a different disk drive."
By moving your installation of Minecraft (all contents of the folder where Minecraft.exe is located) to (in your case) somewhere on your "C:" drive, the launcher should continue updating the runtime environment without problems (the new folder name can be named anything you like).
optional: After updating, you may move the updated files back to their original location.
Hopefully Microsoft/Mojang issues a launcher (Bootstrap) fix soon.
I don't like the forced idea/concept to install everything on/to the System drive...