Someone from NeoGAF got the magazine, PSM3 and there was a feature on F.E.A.R 3 and they decided to summarize the article bits...
I'm not that well-versed with the F.E.A.R story. I have played none of the games but know quite a bit about the story regardless but seriously? That sounds like bad fan-fiction gone wrong!
Alma's pregnancy has opened a rift in space and time. Her contractions are causing shockwaves that are fucking up reality like Half Life 2's portal storms. As her labour progresses the contractions will come stronger and more frequently. Point Man is back from the chopper crash in FEAR 1 and has had time to grow out his crewcut into a homeless-man style beard. Paxton Fettel is still psychically possessing Foxtrot 813's body from FEAR 2 Reborn.
Singleplayer is Point Man only, co-op is Point Man and Fettel. Has a "Generative Scare" system where the Ring/Ju-On style moments are now randomly generated. Fettel can not use weapons but he can stun enemies, suspend them and possess them and can then use their weapons through them. He can also see alternate routes and hidden stashes but the player doesn't have to tell Point Man about them, although the previewers have no idea why you would withold that info. The mechs are still in the game and both brothers get to use them.
Screens looked identical to FEAR 2.