Yume no Tsuzuki./ゆめのつづき。 (Dream Continuation.) is a Yume Nikki fansite that contains an interactive online Yume Nikki fangame created by Rukimi (るきみ) aka Rukimin. (るきみん。) (Blog, Twitter, Nico-Nico User Page).
Important Note: Except for a single post on Nico-Nico, there is not a word about this game on either of these three links.
To enter the game, choose the blue door in the contents menu on the site, then click on the pink circle on the right. Feel free to explore a Yume Nikki-like world using your mouse and arrow keys.
There isn't much of a plot to the game. Your main goal is to simply explore the dream world.