Close Steam then find the shortcut. Right-click on it and click 'Run as administrator'. Login and do whatever you need to do then, find MW2 Liberation and right-click on it and click 'Run as administator'. The reason this happens is because Liberation uses the following code to open MW2:
When you don't run it as administrator, it attempts to open MW2 but doesn't have the permission so all it does is open another Steam window.
steam.exe -applaunch 10190