Your best bet is to ask each game's creator. It's their responsibility to provide playable games. Hope this helps.

Could you give some examples?

I haven't downloaded many itch games, but the ones I have downloaded have never encountered problems like the one you describe.

It could be a lot of different things, if I have to guess I would think you are downloading files that cannot be used on your mac, for example you downloaded a game for android or maybe gnu/linux.

Perhaps they are patches that you must copy over the base game, which will be a different link.

In some cases, they could be bugs.

It's hard to give you advice if you're not a bit more specific, however, the best thing to do is to comment directly on each game.

I think this is a packaging problem.

When I download Linux games on itch, I often get something similar, a directory with a bunch of files, none of which start the game if I double-click on them.  That's because:

• A directory with a a bunch of files is the norm for Windows games.  As a Linux user, I prefer AppImages, and Mac users obviously prefer application bundles, but Windows developers usually don't know how to create those, or why they're useful, or just can't be bothered to do so.
• On Linux and Mac, the actual program file is marked by setting the executable bit on the file system.  Windows does not have the equivalent, so games packaged on Windows often don't have the executable bit set when unpacked on Linux or Mac.
• In order to run the game, you need to find the program file, set its executable bit, and then double-click it to run it.  The command line for this is "chmod +x <file>", and there's probably also a way to do this through the graphical file manager (Finder?).