Distribution does NOT equal installation. For distribution, you can just hand out the needed files (via web, CD, etc.). Since you ask about distributing as a downloadable, that would be over the internet.
Unity games don't need to be installed. They can just be run as is. Many people do like their programs to be in the Windows `Program Files` folder. This can be either done manually, or through an installer program (which can also add a Start Menu shortcut and a desktop shortcut, among other options). There are many installer programs out there, including many free options. As to Windows requiring that the installed program be run as admin, that shouldn't really happen unless you have security settings cranked all the way up.
Again, you asked for *distribution* not *installation*. If you have a good enough game, you can try to get it on Steam and make some money. Otherwise, a simple web server with the game files in a .zip would do.
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