I want to re-download one of my purchased games but when I go to my games there is no menu to download the game. there is just a bunch of things I never heard of before as files.

Welcome to computing. Might I suggest a remedial crash course?
https://en.wikibooks.org/wiki/Basic_Computing_Using_Windows

Firstly, you forgot to tell us how you're attempting to do this? Under your account name via the website, or via that useless pile of code known as Galaxy?

I have never used Galaxy. What am I supposed to learn from your Basic Computing link?

Go to your account, click on the game you want to download, scroll down and find the dropdown menu that says "download backup installers".

They're getting more proficient at hiding away the game exes every few years and it's getting on everybody's nerves including that dude who first answered.

Here are a few links and other bits of information about downloading:
https://www.gog.com/forum/general/download_and_verify_options

Should also mention that if by "a bunch of things I never heard of before" you mean file types/extensions you're unfamiliar with, you should select the correct operating system (right under the title, next to language). Sometimes GOG messes up and changes that, or you might have selected something else last time and it saved that selection.

If when you select Windows, you see files with *.exe and *.bin, and are unfamiliar, here is this:

https://fileinfo.com/extension/bin#gog.com_game_data_file_overview