Um...that's some odd code - and badly indented! You should try to get the indentation right, it makes reading the code a lot, lot easier. And if you are going to use curly brackets around a case code, then put it round the whole code, not just a bit of it - that just looks wrong and is confusing.
char answer;
int choice;
do
{
system("cls");
system("Color F ");
cout << "\t| --------------------------------- |" << endl;
cout << "\t| Press 1 for Playing Game. |" << endl;
cout << "\t| Press 2 Exit |" << endl;
cout << "\t| Enter Your Choice |" << endl;
cout << "\t| --------------------------------- |" << endl;
cout << "\t \t";
cin >> choice; switch (choice)
{
case 1:
{
system("cls");
system("color E");
t.org();
break;
}
case 2:
default:
break;
}
} while (choice == 2);
See how much clearer it is what is going on?
I'd also suggest that the code inside a case should be as short as possible - so move the "play game" code into a separate function, and just call that inside the case. It makes the function smaller and easier to read, understand, and maintain.
Now...about the actual code...
The loop will execute once, unless the user presses 2 to exit, in which case it will go round again. Probably, you want:
} while (choice != 2);
That may fix your problem!