It's pretty straight forward, but yes, I see how it is confusing when only seeing the front end.
- Server starts a game and sets a start word. Word is looked up on the Wiki. If it is found, it is set as the start word. Internally, it saves the URL: http://en.wikipedia.org/wiki/The_Word
- Ingame, the server starts writing the first piece of the game and must use The_Word in his/her text. As soon as the first part is done, he/she gets to choose one of 5 randomly selected wiki-internal links from the page http://en.wikipedia.org/wiki/The_Word by clicking on them. The one he/she chooses (let's call it Word2) is the next word. Internally, the URL http://en.wikipedia.org/wiki/Word2 is saved.
- Once the clients have replied, the server can then once again write a text, this time using Word2. Then, the game picks 5 random links from http://en.wikipedia.org/wiki/Word2 and the game continiues.

This is the simplified version, but it should give you the idea.

Would be awesome if you could try it out! If you try it over the net, make sure to port-forward Port 8080, or use something like hamachi.