I keep looking everywhere, and I do not see any mention of this game ever being mentioned on other platforms. Isn't it weird that a Tomb Raider game, which apparently people say is associated and should remain on Playstation, was first shown at a Microsoft conference, with no mention whatsoever of a Playstation or PC version, no one from Square Enix, their twitter, websites, or any press releases ever mentioned any platform for the game (except for Xbox one at the end of the trailer), and all of a sudden we get this bombshell at Gamescom. Unless someone can prove to me it was in development for something else than Xbox One, we can't just assume. Even games website who posted it for PS4 probably just assumed it would come to all platforms as there is no official mention of it anywhere.
My guess is game was still early at the time (like running on a PC, just like every other game this gen due to architecture), SE having a version not too far along in development,they shopped it around a bit, MS and SE hadn't finalized the deal yet by E3 so everyone kept shut until a later date in case the deal wouldn't go through, not making any mentions of console exclusivity, and at the same time not talking about other platforms. Few months later deal is a go and they make it official at Gamescom. Not very hard to believe IMO.
Also, considering the game broke even for SE, it's not impossible to think they might have seen it as a risky move financially to make a sequel and needed outside help, especially considering how bad they have been doing in recent years. In that case nothing wrong with MS picking it up, just like they did with Titanfall for example.
Also, funny how they made it very clear at the time what platforms Temple of Osiris was coming to!