Mobile game market isn't hard to penetrate. If small game studios like Angry Birds, or a lone wolf developer of Flappy Bird, can make a hit with a title that no one has even heard of, a giant studio with plenty of well known titles under its belt like Activision Blizzard should have nothing to worry about. Their titles practically advertise themselves.
Even the best studios can release a dud, and the King audience is probably very different from Blizzard's traditional audience. What does Blizzard have to offer someone whose only video game interest is Candy Crush? Even if Blizzard were interested in going it alone in the mobile market, they would not only have to build the institutional knowledge about that market from scratch (which is a different proposition for a major business with shareholders to soothe and targets to hit), they would also have to compete with King for that same audience. It's a proposition with high upfront costs, uncertain return, and no guarantee of building a sustainable audience. A division developed exclusively in-house could flop, or fold, or fall short of projections, or any number of other things that could hurt the company's reputation, damage stock prices, send talent to competitors, etc. Acquiring King might be a much safer, though expensive, bet.
I am sure there are a few struggles here and there to get serious with mobile development, but the bulk of the hardwork is the development, porting, and testing, which they can spend some money on, and that money is certainly way less than $5.9B.
This feels more like a political move than business. To say that mobile is the sole reason why AB bought King doesn't quite add up.
From the link you posted, the numbers would seem to add up. A $5.9 billion acquisition that is expected to return $36 billion in revenue by year's end (that seems like a typo in the article, though). You could definitely be right about there being other, perhaps stronger, motivations than investment and return. I've heard that companies with a lot of cash on hand often find it attractive to buy other companies rather than invest it other ways-- it bumps up revenue, lets executives say all kinds of impressive things about growth and market penetration and other jargon, and calms investors without having to take a lot of risks.