Does Steam Family Sharing count as owning a game for DLC activation?

No. Steam Family Sharing allows you to play games from another account's library, but it does not count as owning those games for the purpose of DLC activation. If you try to activate a DLC key for a game you only have access to through Family Sharing, Steam will show the "requires ownership of another product" error. To activate the DLC, you need to either purchase the base game on your own account, or switch to the account that directly owns the base game and activate the DLC key there instead.