While not gamey in the fullest sense of the word, Space Engine allows you to play with the stars. And planets. And moons. And asteroids, and galaxies, and nebulae and clusters and all the sprinkly jazz up there in the sky.
It boasts to sport pretty much everything we know of, and everything we don't know of yet. Procedural, and the scale's not a matter. Sprint among galaxies, dash among stars, and watch the sunset from Mars' surface all doable within the same minute, and mind numbing within that same minute if you stop to think about the distances and the numbers, the size of it all.
You can travel anywhere, and once you figure out which keys control time, anywhen. A quick start hint would be to just start Space Engine, then click on a random star/galaxy, and then press G. Superawesomextrauber ride follows!
It's free. And also still in work. Which means a certain amount of roughness. And the occasional crash.
But all in all, it's absolutely awesome.
Have a bit of patience until you figure out the controls well enough to be comfortable to move around and figure out stuff. And, well, enjoy the ride!