You should sue Polytron for stealing your idea and make millions
The zombie theme plus the unique navigation could make for an interesting survival puzzle game. I really haven't played many survival games, but from what I've seen, they're all about limited resources.
As for the storyline, you could start with the main character and ask yourself different questions about the character to a build a story (i.e. who is this character? where is the character and what is he/she trying to accomplish? What are the character's motives? Is he/she trying to save someone/something? Prevent something from happening? Cause something to happen? Gain power? Get revenge? Find a cure?) Other zombie-specific questions could be: What is the nature and origin of the zombie disease? Is a human/humans behind this or is this spontaneous mutation? Do the zombies have strengths or weaknesses that you can use to add to the story or build strategy into the game? The setting also doesn't have to be a mansion. It could be a prison, hospital, abandoned building, ancient structure, etc.
If you haven't already, I also recommend checking out Pixar's 22 rules of storytelling
As for level-building, navigation could be a key factor in the designs. Perspective is important, and you could use it in various ways for solving puzzles even during combat. Your videos also showed the character pushing objects around. Pushing them over levers to open doors, over cracks in the floor to get across, into holes to fall through to the floor below, in front of pathways to block them, or in other special positions to grant access to more areas of the map. You could also shoot objects or targets to cause things to happen.
As for dialogue, the better you know the characters and their motivations, the easier it is to predict what they are likely to say in different situations in the game. What are the characters' goals, aspirations, and fears? Get to know your characters really well, and the dialogue should get easier.