Like a lot of Xbox's marketing moves, what should have been a positive on their end blew up in their face as a massive PR nightmare.
Here's the thing... even Xbox owners are claiming to be upset (myself included), because this doesn't benefit us either. We were going to get the game anyway. So rather than invest in their OWN stagnating and struggling properties and studios, and improving Xbox owners' experience, they spent those millions simply denying other people fun instead.
This isn't new. Someone brought up the fact Microsoft spent over $400 million securing the rights to an exclusive NFL app for Xbox... the same amount of money Rockstar and 2K Games spent making Grand Theft Auto V.
Microsoft uses money like a hammer, and views every problem as a nail.
They invest in "names" but not in talent. They bought Halo but let Bungie go because they wanted to work on something new (Destiny now the most pre-ordered game in history). They bought Gears of War, but Epic moved on (Gears of War: Judgment didn't light up the charts). They bought RARE and have simply sat on Conker, Perfect Dark, Banjo-Kazooie, Jet Force Gemini, Blast Corps., Kameo, and Battletoads.
This is going to hurt the Tomb Raider franchise, right when it was FINALLY gaining momentum again, and it's not going to convince people to pick up an Xbox One. If anything, like the over 10 million PS4 owners, 80 million PS3 owners, and 70 million Steam owners, it makes non-Xbox owners angry and bitter at the company. It doesn't motivate them to buy a system; it motivates them to hold a grudge against them for taking away a series they loved.
This happened with Resident Evil going exclusive to Gamecube for awhile. Spoiler: it didn't work out. Nintendo hoped the millions of Resident Evil fans would buy the system and get some hardcore gamers onboard. Resident Evil fans didn't show up. The games were the worst-selling in the series, outsold by PS2 spin-offs instead. They lost a lot of money, and Capcom overhauled the whole thing to have less scary elements to reach a wider audience and recoup losses, damage the brand still hasn't recovered from. Gamecube sales did not pick up.
Microsoft apparently didn't study their history.