Their revenue kept growing during this period. It grew by a lot! But their P/E declined, from the 40s to 12 or so. This is because all of the action (iPod, Google Search, iPhone) was happening outside of MSFT. The "growth genie" was gone, and they transitioned from a growth stock to a value stock, and (as perceived) an innovative company to a company protecting its cash cows.
The article discusses whether Google will undergo the same fate. Being the undisputed leader in online advertising is an enviable position; the question is whether Google can grow to be more than that.
And yes, advertising will continue to grow, native/video/mobile are all still growing at double digits and Google is slowly rolling out their products to extract even more value here. The ad industry is going through another revolution and Google, while not innovating, has plenty of growth potential still left.
And this article never said it was. Did you even read the article, or just jump into to defend Google?
Stalled and similar words is not how I would describe them.
Google is not going anywhere anytime soon, it's the defacto unspoken leader in online advertising and the closest competitor these days is Facebook, and even they have a very hard time getting to parity. Google owns so much of the adserving stack and online ecosystem that it borders on ridiculous. Any issues they might face with shifts in advertising would be the same challenges anyone else will face, but Google has more talent, money and scale to solve these problems.