Most of the HTML games here are made with
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. You can download and install it or just run it off the web page. The default story format on Twine is Harlowe, but most Twine games here use the SugarCube story format.
Twine includes several different story formats, so you don't need to download SugarCube separately (the latest version of Twine was just released recently so all the included story formats are also the latest versions). The syntax used vary between different story formats, with different macros and API methods, implementations, etc.
Harlowe is supposed to be the most user-friendly for people who don't know anything about programming, but I've only used SugarCube so I don't know.