What does the 'Play in Starships' button do?

In the game menu of Civilization: Beyond Earth, there is an option labelled 'Play in starships'. It appears to be disabled.

Game menu of Civ: Beyond Earth (press esc)

I know there is a game titled Sid Meier's Starships - does this have anything to do with it?

What is this button, what does it do, and how can I unlock/click it?

Solution 1:

You need to own and install both Civ:BE and Starships
You need to login to your 2K Account on both games, so they are registered there
After winning a game press "one more turn"
The Play in Starships button should now be usable and will transfer your save to Starships
This allows you to start a Starships game with several bonuses.

Here is a list detailling all the possible bonuses: Civ-Wiki

The hybrid affinities essentially grant you the abilities of both, so they are much stronger than the basic affinities you can pick in Starships.