Virtual Networks/Machines are the cloud based alternative to their physical counterparts. There are thousands of businesses that use Azure, or services like it, and they all use it for different purposes. Your question is like asking what Sony would do with a new computer: it's really up to them. 

As I mentioned before, Azure is made to replace physical hardware, and offload the costs and responsibilities to a more specialised service, one that has enough resources to deal with spikes in demand, instant response to security threats etc. Companies have found this a much more cost-effective alternative, to say, hosting their own hardware, employing IT specialists, etc.

Sony may or may not use Azure to stream games. It's doable, and definitely possible...

How does the bolded apply to Playstation though? So far this all sounds very vague. 

That's because it is vague. It deals on a level of technology that very few are familiar with, or even care about. The majority don't care if, for instance, a mobile game runs from Google cloud services or Azure, as long as they can play it.

So far, the only news that we know about is that the deal involves streaming services, and will employ Azure and Azure AI. This is likely to become a service for streaming content from Sony movie studios, similar to Netflix, but I'm sure they'd see the benefit in also employing game streaming in the same platform. It uses identical technology to stream, it just requires a service for input.