Click the MW3 icon that has the "Type Category" Executable Jar File. Once you open it, you should be ready to play. Once MW3 Multiplayer is opened, the little java window should pop up.
PS. In Windows 7 64-bit, I am using. I am able to see these categories;
Name - Date Modified - Type - Size
Arrange the stuff by type and click the " MW3 | 'Executable Jar File' "