This idea is for a far future setting, and would work well with some Lovercraftian overtones.
Stellar Engines are theoretical ways to move a star around… So that got me thinking to how we could use them in a game, other than as a cool piece of scenery. Of course, entire campaigns could be run on one (perhaps as an alternative to a Dyson sphere setting)
In a first contact style-game, the first hint we have that we are not alone in the galaxy is when one of the nearby stars starts moving closer. Do we try and get somebody there, to say hi, or do we broadcast to them, hoping for a response?
For a more Lovercraftian twist, in a space opera setting, perhaps a group of well-funded cultists are tired of waiting for the stars to become right, and have decided to shuffle them into place, ensuring the rise of the old ones? The campaign could revolve about a group of workers working on building the Stellar Engine, who discover that the company doing the funding is actually trying to awaken the Great Old Ones.
In a similar vein, the game can take place once the star has already started moving. Or perhaps the characters are building a stellar engine in order to prevent the stars from ever aligning?