Finally – your long-awaited promotion: Director General of the Department of Agriculture and Fisheries! Located on the thirteenth floor in an unconspicuous office building, many deem it an incredibly boring, bureaucratic job. What they don't know is that this name is just a cover; in fact, you've just become the chief of the country's secret police. And it's not just any fictional or anonymous third-world country, but the United Kingdom of Great Britain and Northern Ireland.
Which should not be read to imply that this is some mostly liberal organisation operating on the basis (or under the constraints) of minor things like human rights or open (transparent) government. It is your task to keep the government in power – by any means needed. You are answering directly and only to the Prime Minister. Every 21 days, your performance is evaluated based on the current opinion polls. If the PM's party is in the lead, your department's funding will be increased. If not, you risk being fired for incompetence.
What makes the game (maybe unintentionally) interesting is that it portrays this job as a pretty average office task. Every day, you arrive at your desk where your personal assistent has already compiled a stack of memos and reports about current events. You read through them; they cover subjects which could potentially influence the public opinion about the government: relatively harmless affairs of cabinet members, bigger environmental scandals, but also terrorist threats.
Each potential crisis is associated with one or more individuals or organisations. The means at your disposal range from surveillance and search to direct assassinations. Some of these possible actions will produce further reports which hopefully provide you with the information you need in order to assess the situation correctly in order to plan additional steps. Other actions will require more delicate followup decisions, like kidnapping a suspect – what level of torture do you want your henchmen to apply in order to get him or her to talk?
The big problem, apart from the questionable moral dimension, with Floor 13 is that all of these events are, of course, pre-scripted. If you have found a good way to deal with a scenario once, it will work the same way the next time you encounter it. And it won't take very long until it will pop up again. Sure, the order the scenarios appear in is randomised and they overlap in different ways each time, but on the whole, there aren't that many.
What saves the game from total mediocricy on the other hand, is that there is a second dimension embedded into the plot/gameplay: Apart from serving the PM, you are also a member of a powerful (and shady) secret society. You will receive additional tasks from the leader there, which will usually contradict the interests of the official government in some way. Balancing those interests, i.e. fulfilling the society's tasks while keeping the PM in power (and keeping your job) is the real challenge of the game.
All this leads to three additional possible endings (apart from being unceremonously fired): If you fulfil all the society's tasks, you will become its new head. If you keep the government in power long enough, you will be appointed Prime Minister (because now you 'know too much'). If your covert operations become too noticeable by the public, on the other hand, you will be eliminated yourself. All these endings give Floor 13 a twist of very dry humour – much needed for such a bleak subject…