Pretty sure this has been reiterated already, but most people call that "Playing online", the only difference being that Microsoft will be responsible for providing the servers rather than the publishers/developers (and from the sounds of it, they'll be providing ALOT of servers, which could allow for alot more npc AIs). There's nothing really new about what they're trying to do, besides possibly the scale of it in a "non-mmo game" (MMOs have done this for years, technically you could say FF11 on console was "running on the infinite power of the cloud" years before the X-Box One arrived).
Its unfortunate that Microsoft got off on such a wrong foot with describing the capabilities of the cloud by describing terrible uses for it (graphics processing over the internet? lol...) because its clouding (pun intended) the genuine uses of it. Having a large number of dedicated servers can definitely make for larger scale "experiences" (for lack of a better word) when it comes to large numbers of AI-controlled NPCs and is definitely something that can be put to good use by developers.
However, making it a selling point is odd because this isn't something that is unique to the X-Box One anyways, hence the ports to 360 and PC. If Respawn wanted to get this working on any other system, all they'd need is another cluster of servers (I doubt Microsoft would be too happy about having their servers used for ports to other systems), which they might not be getting right away from Sony or Nintendo, which I suppose might be the reason for the stated "intrigue".
Game looks and sounds promising however, I just hope it won't require Windows 8 on PC.