@pixelbrain I don't know much about Unity, but from what I can see, it seems like that other game you mentioned baked in the lighting to the model, I noticed that none of the game assets have shadows, only the character does. So if you into "baking", I think you might be able to achieve what you want.
You can learn more about lighting here: http://minddesk.com/learn/article.php?id=54
And learn more about importing to Unity here: http://minddesk.com/learn/article.php?id=24&oid=15
I suggest also reading everything in the "Learn" database, like read everything (it won't take that long). You can find the main database here: http://www.minddesk.com/learn/
If you have any other problems, that cant be resolved by reading the "Learn" database or cant be solved on this forum, then I suggest contacting the developer here: http://www.minddesk.com/contact.php
Good luck! I hope I helped: