I’m going through the whole process, just to be on the safe side: Often times a game is available for more than one operating system. When you download a game make sure that it is the version for your operating system (probably windows). Usually the games on itch come in a packed format (the files end in .zip or .rar). After that file has finished downloading, unpack the game with right click. Then go into the folder that was created and double click the file ending with .exe. The game should then either start or display some kind of error message.
Rarely some games might require you to install some other things first. Those would be listed and linked under “Install instructions” on the game’s page and are free to download and use. (like “requires Microsoft’s .NET v3.5 framework and Visual C++ Runtimes to play.”)
It’s kind of hard to tell exactly what the issue could be from afar… :/ It’s possible that you’re trying to play games that are too demanding for your computer - although that sounds unlikely.
Depending on your situation, the quickest and easiest way might be to ask your friend to have a look. I honestly think they might be happy that you’re showing some interest in their hobby and would gladly help. Alternatively you could list some of the names of the games that give you trouble here. Maybe someone from the community owns one of them and had the same problem.