As the .exe file indicates, you have to make sure you download a Mac OS X compatible game, which means, it should be stated on the page from where you download from, that the game is compatible to Mac OS X and that what you download is the file for Mac OS X.
Can you provide a link to the site you download your games from?
Also have a look at the following links, as the information presented there might be helpful in your future endeavours into Mac OS X and could clear up initial confusion and may even prevent harm to your system or your files.
Mac OS X Basics
Switch 101 - guide with articles made by Apple on how to accustom yourself, after you switched to Mac OS X from Windows
Mac 101 - How to get started with Mac OS X
Find out how - tutorial videos made by Apple on how to do certain thing in Mac OS X
Pro tips - tips made available by Apple for easier ways of doing certain tasks
MRoogle - a very effective tool to search these fora using Google and made available by
edesignuk, introductory threads:
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