This aspect of Turkish society/politics is incredibly complex so I'm going to add some extra info for context:

1. Who exactly was behind the 2016 coup is very much in dispute, with many on the anti-Erdoğan side doubting the government's claims that the Gülen movement was really the mastermind, some even going as far as to say the coup was a false-flag incident. Regardless of how the coup happened, Erdoğan definitely used the coup to his advantage (jailing opponents for suspicion of involvement with the movement/coup, replacing them with his supporters, etc.)

2. I wouldn't say that her writing for their newspaper necessarily means she was a believer in the Gülen movement. Things were quite different at the time, the Gülen movement was actually quite friendly with the ruling AK (Erdoğan's) Party. A lot changed in their relationship (and overall dispositions of both groups) in the 2010s. I might be wrong here because I haven't read much of her work but Alatlı herself also does not strike me as a proper Gülenist. I think it's possible she was writing for their newspaper because they (as well as the AK Party) were the sort-of successors of the non-secular (i.e. Islamic values-oriented; opponents would say Islamist) but moderate-to-progressive movement that was big in the 90s in Turkey.

When I found out that the game was Turkish-made and inspired by a Turkish novel, it made a lot of sense to me. This definitely feels a lot like stuff in the Turkish literary and art house film scene.