It's hardly an obvious move - Google is a Big Data, search and advertising company, not a games manufacturer. They provide services with mass-appeal that users typically use every day or so, like e-mail (GMail), search (Google search), social networking (Google+), blogging (Blogger) and others, but from the perspective of Google as a business these are - fundamentally - all merely ways to deliver paid advertising to consumers.
An Alternate Reality Game is none of these things - it doesn't have mass appeal (most people still don't fully understand what an ARG even is, let alone play one) and even dedicated ARG players spend most of their lives and leisure time not playing their chosen game. It lacks mass-appeal, even dedicated players may not use the service from one day to the next, and there's no clear, obviously way to insert advertising into the game in any particularly lucrative way.
So why release it?
What Google are good at
As stated above, Google are a Big Data company - they excel at managing, querying and manipulating huge datasets, and at making simple interfaces to this data available to the public.However, they also excel at another related skill - getting other people to generate the data for them in the first place.
Remember the free automated directory enquiries service that everyone wondered why Google would launch several years ago? Much confusion was provoked by the choice - "why would they do that? What's the benefit? Where's the business model?", people asked. It seemed mystifying at the time, but Google were cleverly using the service to quickly and effectively build a vast corpus of spoken word queries in a variety of accents, to train the voice-recognition systems that subsequently made it into Google Voice and Android.... and then as soon as it was built, they shut down GOOG-411.
It's worth pausing at this point to reflect on the genius of this move - most commenters were focusing on the (not-inconsiderable) expense of setting up an automated directory-enquiries service. However Google was playing a much larger game, wherein this cost was trivial compared to the value of building a world-class database of voice-samples to train voice recognition software. Not only did they gain a vast corpus of sound-samples, but by setting up an interactive service where users were strongly motivated to correct any misinterpretations (in order to obtain accurate results), they also ensured that they had the correct interpretation of each sound sample - neatly removing almost all of the effort from not only collecting but also categorising/interpreting the learning dataset.
The value of this dataset really can't be over-estimated - Google were already capable of indexing and querying all the digitised text data in the world, but they were completely incapable when it came to audio data - spoken-word, recorded audio, video soundtracks and the like.
By developing an acceptable voice-to-text system they made whole rafts of new application and services possible - automatically generated e-mail transcripts of voicemail messages left via Google Voice, auto-transcripts of video media (allowing both closed-caption subtitles and the possibility of text-searching within video media the way it's already possible to search within textual media), permitting reliable voice search and voice control of software and hardware, and many others.
Or for another example, consider ReCAPTCHA (initially created by an independent company, but quickly snapped up by Google), where their free CAPTCHA service also helped them to automatically resolve edge-cases and unrecognised words when production-line digitising books for Google Books (thereby turning analogue, offline text into digitised, searchable text).
Google Image Labeller was another - a small, fun game Google launched that got users to collaboratively tag images, which in turn hugely improved Google's image-search system's accuracy and specificity.
So how does this relate to Ingress?
At a guess, it's about getting Google good data for footpath routes to compete with Nokia's recently announced turn-by-turn navigation for pedestrians.Google maps/navigation are great for driving directions, but pretty terrible for walking - they typically just tell you to follow the nearest road, which can lead you on annoyingly roundabout, unattractive or even unnecessarily dangerous routes in many areas.Many hints about the new game are dropped in this All Things D article. Note how Ingress is specifically geared around pedestrians:
Users can generate virtual energy needed to play the game by... travelling walking paths, like a real-world version of Pac-Man. Then they spend the energy going on missions around the world to “portals,” which are virtually associated with public art, libraries and other widely accessible places... Outdoor physical activity is a big component of this, though driving between locations isn’t bannedI.e., it's very, very much about walking places... while carrying a GPS-enabled mobile device with a camera and accelerometer and wi-fi and mobile data connection built into it... while running their app that can report whatever it wants back to their servers and has to for you to be able to play the game (i.e., no privacy concerns, as would be the case if they started aggressively tracking and recording the movement of every mobile Google Maps user).
Players walk around footpaths and pedestrian routes that Google Maps currently doesn't cover well, and then as a reward they get to... walk around art installations, libraries and other large, pedestrian-only public areas that Google Streetview cars can't get to. All the time the game client is reporting back to Google their position, speed and the like, so Google gets to build a massive database of popular pedestrian-accessible areas and common routes between and around them. It's genius.
Based on this I also predicted that Google Ingress would also encourage users to take geotagged photos of these various locations in the game as mission objectives. After all, if you've just managed to convince thousands or millions of people to build you a massive GPS-tagged pedestrian-accessible location and route database essentially for free, you'd have to be pretty stupid not to also get them to take geotagged photos and similar media for you while they do it.
I also argued that the game probably records wi-fi SSIDs and a whole bunch of other useful datapoints, too... both proven correct with further investigation in this reddit thread.
Google are very good at manipulating vast datasets, and if anything they're even better at finding inventive and mutually-beneficial ways to convince large numbers of people to voluntarily build those datasets for them.
In short, whatever the plot of Ingress is about, the point of it is to quickly and cheaply build an unrivalled corpus of pedestrian-accessible routes, locations and journey-times for the next generation of foot-enabled Google Maps and Navigation apps, or I'll eat my hat.