Hi Drift Andrei,
Thanks for reaching out to Microsoft Q&A Forum. I understand that you already purchased Call of Duty MW3, but it still requests a purchase when launching.
Please go to your purchase history and confirm that you already purchased it for your current account.
One thing is that you bought the game on the Xbox console; you can't use it on the PC version. The second thing is that you can access the game on your console using xCloud if you have Game Pass Ultimate, thus having the chance to install the game as well as the console and PC versions.
So you can't install the games you have from the console on your PC; you have to buy the PC version that includes the entire Xbox catalog.
You can only install without purchasing if it is through Game Pass.
If you completely purchased both, please contact Xbox Support for further assistance.
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Best regards.