This was a nice little diversion, however I do have some thoughts.
The Mr. House portion of the adventure does not read like Mr. House. I understand that Mr. House's vernacular can be rather troublesome to replicate. But I believe additional effort to get the paragraphs to read like something Mr. House would say in his own words would go a long way.
Missing conflict and humanization of characters:
Once the player reaches the Vault it goes from "brink of destruction" to "sunshine and rainbows" without a transition. I suggest actually incorporating long term characters for the reader to be introduced to when they first enter the vault. With this you can portray actual human responses of shock and panic when the Vault is entered as well continue to use them as interchangeable characters for various other scenarios like the missions, or plot development.
Remember when the scene changes the reader must be informed of the change, otherwise you lose the reader to confusion. When it comes to any form of art it helps to lead the individuals perspective to what you want to show them.
Over all from what I read the dialog is stale, none of it really reads sincere and is wildly out of place with what is going on in the scenario you primed for the reader.
However, I think this shows promise. Perhaps after some time of rethinking the narrative you will develop a more cohesive story that will immerse the reader/player.
Good luck, and I hope this information helps with your progress.