Okay, didn't realize this was the first mod you've ever installed.
When they say FORUM'S ROOT DIRECTORY, they mean your forum directory. For example.
Code:
www.YourWebsite.com/forum/
When they say root, they want to make sure you don't put it anywhere else in that forum's folder.
So basically you'll have your arcade folder located at sitename.com/forum/arcade/
The XML file is something you run with the AdminCP/Products & Plug-ins section.
And to make the links to the arcade appear, you need to do those template modifications the instructions say. The XML product doesn't place links, all it does is integrate the arcade with your forum and database. To make the links, you need to edit your templates that they mention.