Without input from the authors I doubt we'll get a definitive answer but I'll try my best.
As far as I know none of the authors of The Phoenix Project served in the military, however my understanding of the USA is that serving in the army for a couple of years to help fund college is an extremely common practice. In other countries (such as the UK where I live) someone who enters the military often views it as a career and serves for a longer term. In the US it's much more common that people will have some kind of military background.
Question 1: Are these reference to the army background an essential part of the message of the book or just story-telling (e.g. trying to give some depth to the characters by telling their history)?
I don't believe an understanding of military process is required to understand or appreciate The Phoenix Project. So why did the authors include them?
- To illustrate the "rigor and discipline" mentality that Bill started the role with.
- To emphasise the similarities with military practice and repetition which Kaizen values so highly.
- To give small talk for Steve, Bill, and Eric to all talk about when the story needs it
- To give Bill more backstory (see the "opening up" scene)
- To make Bill more relatable to many a large demographic of ex-military personal now working in industry
Question 2: If an essential part, how does the way the US army organises its operations relate with a DevOps culture? Should it be embraced or avoided in the workplace?
This is harder to answer as I have never been in the military myself. However I wouldn't worry about it too much, it's not essential for the story and you could equally draw these parallels yourself with other teams/organisations you are more familiar with from sports, religion elsewhere.
However, as an extreme outsider the US military has a reputation for a couple of things which do apply to DevOps:
- The size and complexity of the organisation
- High levels or organisation in a hierarchical manner
- Enforcing standards and processes
- Creating strong teams (especially the Marines - see Simon Senik's Leader's Eat Last)
Is a knowledge of military required to understand and get value from The Phoenix Project? No. The idea of the military is mostly used as an example for Kaizen, a illustration of Bill's starting point, and to add some character to the erm... characters.