I can’t remember all the details, but I’ll try to summarize:
When Eidos moved “Tomb Raider” to Crystal Dynamics hands Core Design was already working on “Tomb Raider 10th Anniversary Edition”, which was meant to be released on 2006 (true anniversary). They were very excited about it because it was their last chance to redeem themselves after the AoD incident. Core Design didn’t mean to take Tomb Raider back to them, they just wished to pay a last tribute and celebrate the anniversary for the 10 years of the saga. However, Crystal Dynamics didn’t like the idea of letting Core make another Tomb Raider game, so they built a rival demo of their own remake and showed it to Eidos. That’s when Eidos cancelled Core’s project, but I don’t think they’d ever made an official statement explaining the reason behind that decision.
Sorry if I can’t give you more information about it. In fact, most spanish fans including myself had NO IDEA about this game until quite recently. It feels as if Eidos wanted to keep it secret. So I strongly recommend you ask @tombraider-of-coredesign if you have any doubt about it, they’re way more aware than me about these things.