Apple is in the content delivery business.
ipads, ipods, iphones, itv(appletv)
All of which focus on delivering content of some kind to the user. Music, movies, apps, tv shows etc.
Apple hasn't been interested much in the content creators, but more in the delivery medium. They've found a nice niche in human interaction and charge a premium for it.
The one area they have failed, is in the home.
One could argue that ipad sales are making inroads there, but I would counter that ipad is still a personal device and is more likely to replace a magazine/newspaper than a TV.
AppleTV would obviously like to fill this void, but Apple failed in its previous attempt to dominate the livingroom with the first version of this product.
Granted, the hype surrounding Apple these days is greater than it was then, but I still think the product doesn't offer enough for most people to want to purchase.
So, Apple still needs some way to get into the livingroom of the typical family.
Apart from some dramatic venture such as robotic butlers or buying every tv manufacturer on the market, I'd say their best bet is go with a business which has a proven track record of entering livingrooms by the tens of millions.
Gaming
Wii has shown there is a huge interest in gaming outside of the typical hardcore gamer we think of traditionally. Reports of grandmothers and wives were reportedly not only interested in gaming, they were buying the Wii in droves.
Playstation2 proved the gaming landscape stretched well beyond 100million gamers last gen.
The other interesting aspect of gaming is the audience that grew up with gaming is getting older, but younger kids are always going to be interested in games. Some of the population will indeed grow tired of gaming, but some will not and therefore the market is ever expanding
as long as the price is viable.
Apple could very well decide to try their hand at putting together a gaming box on their own as MS did with xbox1, but I'm sure they also saw that mistakes can lead to huge losses and it isn't cheap to build a brand in the gaming world.
One thing I'm sure of is that Apple will not acquire EA as a standalone move. They aren't in the content creation biz. If they acquire EA, it will be as a foundation for 1st party titles.
And with that, I say, "Welcome to the gaming biz, Apple".