The word "process" is used in the article, and in this thread, with many different meanings.
Humanistic Psychology defines process similar to how the author describes 'culture'. [1]
Take ceramics, for example. "Process" is working wet clay on a wheel with one's hands. It extends to the atmosphere of the studio – the mood that the artist creates in their environment (what music do they listen to, what is the lighting like?).
Humanistic Psychology posits the most beautiful products will emerge out of situations in which the artist is fully immersed in their process. The process itself is the goal, the products are 'by-products' whose quality is determined by the level of joy and concentration the artist brings to the process.
Tribal dynamics, also mentioned here and in the article fit into this model as well. According to Phil Jackson, NBA coach with eleven championship rings, a beautiful system (or process) is the key to success. [2][3] In the case of the Bulls and Lakers, this consisted not only of the triangle offense, a system that promoted a pure style of basketball playing which involves the entire team, eschewing traditional 'plays', but also extended to the way the team practiced, meditated together, had fun together. In this sense, process and culture become the same thing.
1: The Farther Reaches of Human Nature, Maslow. http://books.google.com/books/about/The_Farther_Reaches_of_H...
2: Eleven Rings, Phil Jackson http://www.barnesandnoble.com/w/eleven-rings-phil-jackson/11...
3: Tribal Leadership, Logan, King, Fischer-Wright http://www.amazon.com/gp/product/0061251321/ref=as_li_qf_sp_...