Learn English – What does this mean: To be thus is nothing; But to be safely thus

In this context, for the specifications to grow organically means there is no overarching control or direction. Each developer writes their own tests, without consultation with or approval of a higher authority. Metaphorically, it evokes an image of a tree or plant which grows outward and higher from the bottom up. So the phrase describes a "bottom up" process, as opposed to a "top down" architectural or dictatorial process.

So you see, your final question "Does it mean to grow dynamically with changed requirements or get modified with changed requirements?" isn't really addressed by the phrase. It simply means there is no single authority which dictates the specifications. They will arise (grow organically) from each developer's tests.

The second sentence is expressing that the quality of mountaineering journals' content rivals that of the best English-language essays. That the writing is a cut above what you might find in, say, a fly-fishing journal computer gaming magazine.