What you have there is a compressed file which needs something to decompress it. The usual tool of choice for the Mac is Stuffit Expander which is part of the OS.
When you double click on the .sit file, Expander should launch. If it doesn't you need to find it from the list of applications that appear. Stuffit Expander lives in the Utilities folder on your HD. Choose that application and it should decompress the .sit file. Once decompressed, it will leave another file which may be the actual application or an installer. Forget about the .sit file now. If, when you double click it, the game starts - quit the game and drag the icon to the applications folder. If an installer starts, follow the instructions and it should put it in the Applications folder.
If the program is iHearts 4.1.1, then once it is decompressed it will leave a folder with the App inside. Expander will decompress to the same location as the original compressed file. Drag the folder to the Applications folder.
Play the game
Hope this helps
I downloaded, or think I did, ihearts macosx.sit and have that on my desktop and when I Click on it it goes to a window and says choose application and under that it has mac hd and steve's mac mini. I choose mac hd and under that it says applications and under that it has adobe p, apple script, apple installers, iphotos and others. Tell me how to get the games where I can play it please. As you can tell I don't know too much about this mac or computers in general. thanks