Ok, your essay is quite creative idea. Game is not an often approched topic. It's wise to choose to write a simple game rather than a complex one. But still few problems( My Enlish is not as good as you so don't be too serious. I just want to be help)
1)
Snake is possibly one of the greatest games of the 20th century.
The opening need improve. What about begin with " left, right, up and down..." If you really want to introduce the game, do it in a more absorbing way.The first paragraph doesn't make sense.
2)
I was at first skeptical about the captivity of this game, but it was not long before I began to see the wonder and excitement involved.
Don't tell, descript what was on your mind at that time.
3)
Yes, getting the highest score in your math class is thrilling, and I was ecstatic to have been named one of the top scorers in the IB program of our school.
It seems you just want to tell the fact that you are an excellant studnet. You need to join this with your theme,like ...thrilling, just as whant I have experience in ...
4)I like the fourth paragraph very much. Please expand it if you like. Write about what you felt we the girl outdo you and why you want to exceed her so much.
5)Finally, I guess you forgot the your initial purpose to write this essay. The resemblance between the game and your life. I'm sorry you didn't include the idea in the second version. It's the element make your essay stand out. If you reuse the last paragraph of your first version, I will suggest a title : Sneaking Forward
If I were the one to write this, I would write in this order
1 Descript a playing game scene
2 Remember the your story with your competitor, your effort, your growth during the process
3 The resemblance of the game and your life.
4 Make an open ending, not a cliche one
Ok,that's all. I guess have to go.