Do I have to separately install the Immerse Gamepack Call of Duty to enable in the game?

You don't have to install any separate application to listen to Immerse Spatial Audio inside Call of Duty, it is directly integrated inside the game.

Please follow the below steps: 

• Launch the Call of Duty game application, go to Audio Menu
• Go to the Audio Settings in the game’s options menu.
• Enable Enhanced Headphone Mode.  You can now listen with a Universal Profile.
• Click on Configure Enhanced Headphone Mode 
• Scan the QR code and follow the process on the screen to finish creating your Personalized Profile.