Ahhh.. gotcha :p
That is coming up with that message because it looks like you're trying to apply for membership to a site you're already a member of ;-)
It certainly makes checking out your application form a challenge :p
As you can see, you're already logged in in that screenshot, and you are a member of that site as otherwise you wouldn't have the admin options available to you.
What I see, on the other hand, when I click the "Apply for Staff" button is:
I think you could possibly test how it looks by creating a new account and going partially through the process until you get to this point. I don't know, off the top of my head, if there's another way of previewing it.
Is this what you mean:
If so, there are a couple of links on that page that allow you to login if you already have an account (one above the Facebook button, one below the "create account" button). If you don't have an account with GL, then you can just fill in the forum and click the "create account" button.
So I set up an application, but every time I try and access it, it asks for me to log into either Facebook or Steam. I don't have FaceBook and don't want to add steam. Is there a way to turn this off, as I don't want my members having to connect Social Media to the website.