This is not the key. The DLC is sent as a gift. VPN alone is not enough to activate the DLC. You must have an account in the respective country. Account country is indicated on the page https://store.steampowered.com/account/ in your account settings. If you have a different country on this page, then you will not be able to received the DLC.
How to activate Steam Gift:
1. Download and install the Steam client - http://store.steampowered.com/about/
2. Register a new account or login as an existing one.
3. Copy the link to your Steam profile in the specified field when buying the DLC.
4. Tell the seller a unique code
5. Wait for an invite to friends of the seller and take it.
6. When receiving a notice of sending you a gift take it.
7. After adding the Library to start downloading the DLC and wait for full load.
8. Enjoy the DLC!
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