Judging by a job listing at Microsoft Careers (now taken down), it looks like the company wishes to create an open source framework that is lightweight, extensible and scalable across multiple platforms, specifically naming the mobile platforms from Apple and Google. Since Xbox Live is integrated with its Windows Store and Windows Phone already, it looks like Microsoft wishes to do the same with iOS and Android.
Reports point out that Microsoft is also trying to win the hearts of game developers by working to provide improved tools for Xbox Live integration. Reports also indicate that Microsoft may ease up on restrictions and provide greater access to the necessary tools.
It could be a win-win for both sides. If Microsoft plays its cards properly, it can attract a good number of developers. Since Xbox Live will be present on almost all mobile platforms, the game achievements, scores and even ability to play games with their friends can be crossed over/shared/ played irrespective of the mobile OS. Though iOS and Google have Game Center and Google Play which shares scores and game achievements, its uncertain how does Microsoft plan to get ahead of its competition.
But having a cross-platform service is what can rule in Microsoft's favour. It will allow easy access to gamers irrespective of the mobile platform.