Overally, it looks pretty good. I'll point out some things, though.
Girumon wrote:十二月二十四
You're missing 日 after 四.
Girumon wrote:テレビゲームしか何もしませんでした。
You don't need 何も here, and I wouldn't put it there. 「しかない」 implies "<whatever> and nothing more" already.
Girumon wrote:テレビゲームは楽しいですがそんな事毎日したら直ぐにつまらなくなります。
I would take out そんな事. And I would replace つまらなくなります with 飽きます (飽きる[あ・きる] = to get tired of).
Girumon wrote:最初にプレゼントをあけました。
I would say 最初は instead of に. Don't ask me to explain why. I'm not sure myself exactly. It just sounds more natural to me here.
Girumon wrote:私は衣服とかテレビゲームをもらいました。
A couple of points here:
-I would just say 服 here
-とか is a bit on the informal side. I'd stick with や
Girumon wrote:過ぎ
過ぎ should be 次. つぎ not すぎ
Girumon wrote:とてもおいしかったからもうすぐお仲が一杯になりました。
-お仲 should be お腹
-grammatically, it's fine, but the logical flow is slightly off. Maybe you're different, but I've never gotten full just from food being tasty. You may want to slip in "I ate a lot" after から