Are gifts given to you for your birthday legally yours?

For my 14th birthday, my grandparents bought me an Xbox 360. I had been begging for it for over a year. I remember standing in the check out and grandpa joking "this will be your only birthday present this year" and I recall that we bought it just after skyrim came out, which was about two weeks before my birthday. They are angry that I am moving out, and have decided to keep my Xbox. Grandma is now claiming that it was not a gift and that she bought it for any kids visiting the house, and I can't have it. Even though it was a gift to me, I offered to buy it off of her, or to buy her a New Xbox. She refused. I pointed out that the total of all of the downloaded stuff I put on it totals $267, and that I expect to be paid back if she keeps my Xbox. She laughed in my face. Not that it changes the legality of her taking a gift of mine, but I'm not just some brat that wants her Xbox. It has a lot of sentimental value to me. When I was 15, my best friend killed himself. I created a minecraft world with all of our inside jokes, references to his interests, quotes of his, and just overall things I want to remember about our friendship. I don't remember things well, so I created that world to be able to remember. I told my grandma this and she still doesn't care. I have checked, and I can't take the hard drive or transfer the data to a New xbox. I'm moved out if it matters. Please help, if it was just for games I would buy a New one. I can't lose all those memories with my friend.

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