....the meaning of the word 'gift' in the secret ending.
I have remembered that in the Gamescon trailer of the game, the narrator says at the end of the trailer something which is a big hint regarding the meaning of the word 'gift' :
'' On dedication of her third birth, I offer her this gift to she, who has awaken from her lost past: Aya Brea. As humanity remains trapped in time square (don't know what this means), she is their sole hope. Perhaps it is she that is the gift to us''
What I have thought it's that this sentence has a double meaning: what it means is that Eve is not just literally the savior of humanity, but she is also the gift and savior to them because she is the only one whose mithocondria can be implemented in other humans without turning them into monsters, and thus humans can become immortals like Eve and Aya.
If you remember PE 2's plot, (SPOILERS) the organisation of the Shelter tries to transfer Aya's powers by using her mithocondria, but this doesn't work well, people became monsters after recieving Aya's mithocondria. In PE (Spoilers) Aya has powers thanks to her dead sister's cornea and Melissa thanks to Maya's kidney, which could mean that they haven't initially turned into monsters thanks to those organs with Maya's mithocondria.(END SPOILERS)
This game's plot makes a reference to that plot element when it is stated that the Twisted can reproduce but in exchange of it they lack inteligence, while the High Ones are a inteligent species but they are a few people.
To conclude I think the narrator in the trailer is talking as Kyle, since in the secret ending Eve says ''A gift from the two of them'', where she refers to Aya and Kyle, something which is related to the trailer's sentence ( '' I offer her this gift'' ) Moreover the trailer ends with a quote of Kyle: ''You'll see her again. Come to the Babel in the red fog.''