(I'm an Australian lawyer and will use 'trade mark' as my preferred spelling.)

The headline of this link is misleading. An action doesn't 'violate a trade mark'. An action can infringe the rights that a trade mark owner has (the scope of those rights will be dependent on the location in which the right has been granted and where the action takes place). In common law countries, trade mark rights can refer to statutory rights (which are granted in accordance with a piece of legislation and typically require registration with a government office) and common law rights.

This document is Adobe's guidelines for use of its trade marks. Adobe is saying that, if you follow the guidelines in these documents, then you can be sure that you have not infringed any of Adobe's rights in its trade marks (or at least that Adobe won't sue you alleging that you have).

Whether a failure to follow these guidelines constitutes trade mark infringement is a separate matter. Generally speaking, a trade mark owner has the right to use a trade mark exclusively in the course of trade in respect of a class of products. What does it mean to use a trade mark in the course of trade? This means, for instance, using a particular word or phrase to identify your product. Consumers will then use your trade mark to identify your product in the course of trade (eg. 'Could I please buy a copy of Photoshop?'). An obvious rationale for trade mark rights is to protect consumers from unscrupulous merchants who might call their product Photoshop in order to take advantage of the goodwill Adobe has built up in its product.

However, not every use of a term is in the course of trade. It is not in the course of trade for me to write a Wikipedia article about Photoshop. I would argue it is also not in the course of trade to use photoshop as a verb to refer to the act of digital manipulating an image (such as by using the Photoshop product).

Why does Adobe want to prevent people from doing this? As others have pointed out, if a trade mark falls into common usage, a trade mark owner can lose the ability to register it as a trade mark (trade marks are usually registered for a period of time and must be renewed after that period) and so lose, at the very least, the statutory rights associated with that registration. This then enables competitors to use that term in their products. Good examples of trade marks that have fallen into common usage are elevator, xerox and hoover. Obviously Adobe spends a great deal of money developing and marketing the Photoshop brand. They do not want to see it become a generic term that competitors can use.

That said, usually both trade mark owners and their competitors have little interest in a term becoming generic. You don't see Microsoft going around saying that you should 'google' something. While a trade mark falling into common usage can be a bad thing from an intellectual property perspective, it can of course be a good thing from a marketing perspective. This is why the only people like to cause a trade mark to fall into common usage is the general public (and possibly journalists). So, people like Adobe pay lawyers to draft up these kind of documents to help make sure that doesn't happen.

While I practice law, I must give one of those annoying disclaimers that are part of the reason people hate us: I am not your lawyer and the above should not be treated as legal advice. If you are concerned as to whether you are infringing a trade mark, I recommend speaking to a lawyer in your local area.