Sure, but the solution helps with both (bandwidth because they only need to stream data once over the internet to each data center, not once for every client connected to that datacenter; and latency because there are fewer hops between client and content source).

An infinitely-resourced online play service could pay to install machines that run the games the same way Netflix pays to install their streaming boxes, and would care about both latency and bandwidth (since more bandwidth => better resolution video).