Yep. They want to avoid it becoming generic. They're far too late, though, to stop photoshopping from becoming a verb because these guidelines have been completely ignored by almost everyone for a long time now.
It kills the trademark. Once something becomes generic, anyone can use it. So a competitor could say "we produce the best photoshop software" because the term is now simply a word for editing photos digitally rather than for a specific product from Adobe.
Because once it become generic, other people can start selling products called Photoshop. Suddenly, there'd be Microsoft Photoshop and Adobe Photoshop and Canon Photoshop and who knows what else, and they are afraid they'd lose their dominance in the market.
Having a generic brand name doesn't mean other companies can do that, as there is no legal term defining generic brand names (i.e. a brand name that became synonymous with a product). What does happen is that people start referring to other products using the brand name, and you might lose the identity of your product.
If people use "to google" for performing an Internet search, it can mean they will automatically use Google.com, which Google want, but it also could mean people will start "google" stuff using bing, or duckduckgo.com and if the term becomes generic enough, it will lose the immediate attachment it has to the actual search engine.
Another issue is that it carries connotation. When you say "This model was photoshopped to look thinner/prettier/etc." you create a negative connotation with the brand. Adobe fears people will hear "photoshop" and immediately think "falsifying images, creating false reality, hiding stuff" etc.
It also causes the brand to be identified with a single product, which in Adobe's case is not such a huge deal, as Photoshop is the product, but in other brands, like Apple, or Google (again), means a whole slew of products across different fields, this is also why the Apple sign was removed from the Macintosh' keyboard.
Having a generic brand name doesn't mean other companies can do that, as there is no legal term defining generic brand names (i.e. a brand name that became synonymous with a product).
Actually, it means exactly that-- as you can tell by the number of companies selling "aspirin" or "cellophane" or "linoleum".
Trademark is precisely the protection that prevents others from selling a product with your name (or one so similar as to be easily confused.)
