Not true at all - their share price has more than tripled in the last decade [0]. Web development was never a big part of Adobe's business. They were trying, because it's similar to their other product areas, but they never got a big foothold, except Flash.
They still make a ton of popular software (Photoshop/Lightroom, Premiere, Acrobat, Illustator, After Effects, ...), and most of it is selling better than ever.
Flash In The Pan: Historical Lessons Of Adobe's Macromedia Acquisition https://adexchanger.com/data-driven-thinking/flash-in-the-pa...
Adobe accused of software monopoly (not by Apple) http://www.techworld.com/news/apps/adobe-accused-of-software...
The Real Story Behind Adobe’s Failed Mobile Strategy http://www.businessinsider.com/the-underlying-story-behind-a...
Adobe recovering from massive Creative Cloud failure (one of several) https://www.engadget.com/2014/05/16/adobe-recovering-from-ma...
The Agonizingly Slow Decline Of Adobe Flash Player https://www.fastcompany.com/3049920/tech-forecast/the-agoniz...
And, finally, some commentary on the nature of Adobe's stock rise: http://www.forbes.com/sites/petercohan/2014/02/28/why-is-ado...
Adobe Systems Inc. May Be Wildly Overvalued http://www.fool.com/investing/general/2015/09/29/adobe-syste...
Adobe Is Extremely Overvalued http://seekingalpha.com/article/2675425-adobe-is-extremely-o...
Adobe: Overvalued Despite Improving Profitability http://seekingalpha.com/article/3989440-adobe-overvalued-des...
But to be clearer, let's rephrase and say that "Adobe the company has had a rough decade".