Once again, Kingdaro, YOU DO NOT NEED TAMPERMONKEY ON CHROME!!! Chrome has this functionality built-in and treats userscripts as regular extensions.
No, you don't need it, and I've run scripts without it before, but you should install it anyway because it adds a lot of really great features like site white and blacklists, editing the script in the browser, automatic updates, etc.
I had so much trouble finding this topic today. I don't normally read the drama forum.