Microsoft has licensed ARM's architecture, but while an ARM might be found in every mobile phone it seems Redmond is more interested in putting some ARM goodness into the Xbox.
Nintendo uses ARM chips in its mobile consoles, but it's hard to imagine Microsoft making a play in that space given how hard Xbox Live is being pushed as a feature of Windows Phone 7.
The Xbox line, however, is in serious need of a new architecture. Microsoft's approach to gaming consoles (and computers) has always been to have a whopping great chip in the middle doing most of the work. The Xbox 360 still suffers from the concentration of heat that this approach creates, depending on a heatsink that expands and contracts until it eventually touches one of the chip's contacts, shorting out the system.
Increasing the processing power for the next incarnation of the Xbox will need a different approach, which is the most likely reason for Redmond to want access to ARM's innermost secrets.