I don't see how this classifies him as being a brat. He just wants to move so that he's not distracted by an obscene amount of noise.
Whinging about sharing an xbox with your brother = brat. this kid is taking his setup for granted
Buy your own desk
I really doubt he's old enough to yet.
That is if he is old enough to move out/has the funds too.
The reason why people are giving you hell in here is because being upset that you have all these nice things that you have to share with someone else is a really bad attitude to have.
I had the same problem bro I suggest saving your money to get a desk in your room!
At least you have that. Not trying to sound like mom or anything, but you should be thankful for what you already have there.
I dont know how old you are but demonstrate to your parents that you are seriously into computers. It would be bad parenting to not nurture that skill in a child. That desk looks like something used occasionally for finances and logistics by your parents. Tell them its time to set up a real office space in the house.
The reasons you gave in this post seem like a good place to start. I assume you have done this already so I would tell them you need a nice place to relax and have fun, and that is not possible there for the reasons you gave.