All software, when run, resides in RAM. Most apps and games specify the minimum amount of RAM you need to install them and run. This amount includes RAM that the computer needs to do its own background work as well as to run the app. So if a program says it needs minimum 1gb to operate, it'll run fine on a system with 2gb. However, I would also pay attention to the "recommended" memory which would be the RAM required for optimal performance of the program.
Generally speaking, memory requirements are specified taking into account the requirements of the application, operating system, supporting software and files, and other running processes.