It is. Some studios actually do this (e.g. Blizzard, High Moon, some had done it before they had been shut down). The problem is that Agile has been designed for a process at a service firm, one that does work for hire. As far as I understand, in that business you don't really want to ship. Instead of shipping you want to keep your customers engaged and paying your invoices as long as possible, preferably forever. This can also be useful for a firm that provides continuous service since there is no shipping involved too. And there is nothing wrong with it. But games have to ship. Continuous development without a hard shipping date is called "development hell" [1] in game industry.
From what I've seen Agile does not work very well here, at least on the engineering side. Design might be doing something similar to Agile on a small scale.
Of course it is. You can see the strategy of rapidly iterating on game mechanics first, for theoretically releasable, yet too crappy for the market, in interviews of old school devs: Sid Meier and Peter Molyneux built their first hits this way. Today we also see this approach in Early Access games on Steam.
The reason we don't see it everywhere though is because in AAA games, deadlines are seen as something so important that large parts of the game are built simultaneously. In your typical modern story-based action game, you have different teams working on different levels, and some people might spend all their time in just one or two levels: To get that level of parallelism, and have over 100 people working on a game, chances are that the development process will not have much to do with agile.
But many of the games that most people would consider great come from much love, refinement and iteration, along with relatively long development periods. This is why Blizzard always takes forever, and we have the concept of Valve Time.
From what I've seen Agile does not work very well here, at least on the engineering side. Design might be doing something similar to Agile on a small scale.
1. https://en.wikipedia.org/wiki/Development_hell