Hey, ChiefinCharge!
Welcome to the forums. I can see that you have the Steam version of Rainbow Six: Siege, as such do you have any controller settings in Steam enabled?
In Steam, click on the Big Picture Mode button in the upper-right corner
This will open Steam in Big Picture Mode in full screen
Click on the Library button
Select Rainbow Six: Siege
Click on the Manage Game button in the left-hand column
Click on the Controller Options button
Click the Steam Input Per-Game dropdown box
Select Global Settings
Launch Rainbow Six: Siege to confirm that you can now use your keyboard
If the issue persists please let us know.
Thank you.