When you say strategic, the first thing i hear is "move units over a map to pew-pew other units." so likely you'll end up in another genre if you don't want that.

How about every planet in your empire has it's own characteristics, that you have to balance out?
- the species living on it can give bonus to internal security and reaction-speed to your orders

also the loyalty-changes are bigger/faster for some species.

- the type of planet enables mining of certain materials

- the atmosphere will determine which species can potentially live there

- the governor will gives speed to development of new....umm, let 's say factories for now

planets have certain needs to keep functioning properly(usually this is called happiness or morale, but it should be something more then just the sum of satisfied needs vs. unsatisfied needs; for example a present army would give more internal security, better chance on stopping a revolt if it happens, but not pre-emptively stopping a revolt,
they will also decrease morale on the planet if there are not enough brothels available, and off course they'll have some (other) kind of upkeep-cost)

and they need resources for that that need to be transported and consumed.

Now let's say there are space-pirates that you have to deal with, but they're too strong to just wipe out.

A player needs to get resources past them without being intercepted(cloaked freighter, pay the pirates off, take a different route, just let a planet perform less for a while?)

and sometimes the pirates will bond together making a big fleet and attempt to pillage a planet.
(I recommend against a success/fail approach and just assume that pirates will always deal some damage to the sociological structures of a planet,
but how much would depend on defenses and such)

Notice how there are still fighting units moving around(pirates) but the player controls the counters(resources, governors, certain laws) to them.

As a side-note, in MOO2, i often had my fleet protecting whichever star-system was still under development, since the other star-systems were usually capable of defending themselves, it was actually not very strategic that way imo, but for the game you want such a strategy might be what you want with your fleet
(aka they're just at one place defending/building there so you can expand in the long-term, while the actual fighting/interacting/strategy happens in the rest of the empire)

If someone makes a game they should have their facts straight.

Haha because this is something that breaks my immersion in a fictional game world, it's accuracy when considering social contract theory. I remember the last time I played a game and thought why is the governing body of this city letting me just kill this hooker and take this floating money and only sending one blood thirsty cop to drive me off the road and kill me?

Property, governing, power and the ruse of authority. Call it all what you will(monarchy, empire, corporations, government, civilization, etc) and feel free to complicate it as much as you like with modern law, but the fact is we're all slaves to the notion of ownership and fooled by the idea of power. It's all just socialization from childhood that helps to keep this broken thing we call civilization going with it's anti-economizing "economic system". When in reality any programmer worth their salt, willing and able could build a better resource tracking, accounting and allocation structure along side automated production and distribution systems better then any capitalism focused governing body, globalized market exchange economy could ever hope to match. Providing more goods and services more economically to everyone on this planet, educating more people, advancing technology faster and more efficiently and offering better health care all the while better sustaining this finite world and its fragile structure. Tangent rant complete! On to more important matters then saving the world from itself.

how exactly such mechanic should work

Depends on the scope of the game but you could limit the entire game to a single(throne) room or expand as much as to explore a sandbox across multiple kingdoms. Depending on how many visual assets you feel you can get done along side the code and their use in displaying the plight of the kingdom. I was thinking of something like Fable III combined with more social/choose your own adventure gameplay. NPCs(peasants, nobles, military, spies, etc) bringing the issues of the kingdom before the king, using a back end economic system that enables the player to exercise economic foresight and upkeep the kingdom. A conflict map to display the armies and known enemies of the kingdom and a council table to seek insight from "experts". Challenges could include the uprising of most if not all of the kingdom(uprising nobles), a foreign threat, a none human threat(monsters or pests), expanding the kingdom or any combination of those or other plights of a civil population. Win conditions could include military might, economic prowess(buying allegiance), emotional manipulation (kidnapping, torture, winning the heart, winning the mind, etc), death of a single powerful foe, death of an idea or again a combination of these or any other strategies to win and hold the hearts/minds of the populace. To boot mechanics to keep your character happy, healthy and to protect your legacy could be a nice addition as well.

The game could be about gaining wealth and power for your family, the imperial family grows over time

(well, if you piss off the population assasinations and/or riots might change that)

and as player/emperor you try to put its members into places of power in the empire.

Usually this will gain you a slightly more loyal servant, yet much more incompetent compared to the "right man for the job,"

who was also available(choosable for the player) to take on the job.

The purpose of this may be so that the next emperor, after a long and bloody powerstruggle, will come from the old emperor's family as well.

This would be quite realistic but make it a "survival-game" which most players don't like.(as the Moldy Cow pointed out)
Make it too easy and it is a sim-game.

Another purpose might be that the imperial family has the ability to recognize "the enemy infiltrators" and destroy them,
and the goal would be to destroy "the enemy infiltrators" or remove them from power.
These "enemy infiltrators" may be anything ranging from spies from another empire to vampires spreading over the population to another rival family.