It's a losing battle, but I suppose they have to expend the effort if only for form's sake.
Google wants people to only use "google" if they actually use the Google search engine, so no saying, "I googled it" when they use Bing or Yahoo! or Dogpile or some other search engine.
There's a lot of precedent against them: Kleenex tried it, and lost out. Now people call all paper tissues "kleenex". Xerox tried it, but the weight of people saying they "xeroxed" a paper made the term generic.
The article also named aspirin, escalator, and zipper as previous brand names that have become so ubiquitous that they transcended the brand to stand for all products in that category, regardless of the other companies that also make similar things.
It's got to be a rush to know that your product is so popular that it becomes a household word, that it trumps all the other manufacturers and their brands.
And scary, too, that when you gain household word status, you lose control of your brand.
Except, Otis Elevator Company (who gave us the word "elevator") is still operating, still making and servicing elevators, and still profitable. There's Shindler, Crescent, and Modular Elevator Companies, too, but they are johnny-come-latelies and no one pays much attention to the manufacturer of the elevators unless they're buying - and you can bet most architects and construction firms know Otis is first and still best in the elevator field. Becoming genericized has not hurt them.
Kleenex brand tissues are still made and sold, and becoming a household word didn't hurt their business. I remember the law suits when Kleenex tried to maintain control of their brand, but in the end, the word "kleenex" means both Kleenex brand tissues and disposable paper tissues of all other brands.
Google is taking rank with some pretty respectable companies, and while they feel they have to raise a fuss and pursue a few legal cases, in the end, the power of the people will prevail and "google" (lower case) will always be the term we use for looking things up on the internet, even if people used Bing, or Yahoo! or Blekko or YaCy or Zillow or Nexis... It's a catchy, memorable name.
It was their goal to become ubiquitous, and now that they've achieved it, they have to make a show about maintaining brand control, just like Kleenex and Xerox did back in the day.
Welcome to the Überwelt, Google. I'm sure Kleenex, Otis Elevators, Xerox, Bayer Aspirin, and Goodyear Zippers will make room for you and you'll get used to being both a Brand Name and a household word.