I'm trying to download XNA game Studio, but at the moment I try to install it it says this:
Note: The Hyperlink sends me to a microsoft site to download VS2013 Express edition.
I'm on Windows 8.1 x64 with a full-component installation of Visual Studio 2013 Ultimate edition.
XNA Game Studio has not been updated in many years. It requires VS 2010 C# Express or VS 2010 Pro+. There are some hacks on the Internet about how people have gotten it to work with VS 2012 and VS 2013, but it's only officially supported for VS 2010.