> highly dogmatic, stubborn and difficult-to-get-along-with people
Not a problem. They have a way of doing things. That is their way. If it is wrong, how do we persuade them?
> They might even shout or yell at other people to get their own way.
Not good. It becomes a personal problem, and people forget their roles as problem solvers, and turn it into becoming winners.
> Such people find it hard to empathise with others and think they they are the smartest and that their opinion is more valuable than everyone else's.
Key word here is 'opinion'. Can it be changed to fact rather than opinion? Opinion is personal. Break it down and go back a/several steps, to get logic out of the opinion. If they're getting personal, as above, this may take hard tactics, but being non-personal is key. Open questions, act as the idiot if you're in a position of authority.
> They value "the right technical decision"
Great. They're committed. They want the best answer, and rationality is the appeal [key - 'from their perspective']
> over human relationships
Bad. Perhaps they're engrained and don't recognize other interests. Take the conversation back and get them to focus on long term interests. This can be interesting, as often you may find the 'suborn, non-team-player' is trying to act in everyone's interests, they've just made it a personal 'win' and others don't recognize they recognize the win-win but are so engrossed they don't express it (or there's a small thing they're afraid of giving up).
> the right outcome might be the one that makes someone else happy, or is the most diplomatic
Negotiation is not win-lost. It is win-win. Often the term 'diplomatic' puts someone in the losing corner "give this one up for the team, we'll win at something else". That is not diplomacy. Diplomacy is recognizing there is a problem for everyone and giving something up is not a good option. Stick to facts, logic, and encourage the exploration of everyone's long term interests. Remember, you're problem solvers. "Technically right" often is right. Information is key here - is someone unaware of a constraint in budget, personnel, timeline, or other? Lacking information makes one feel weak, and emotionally responsive.
> How do these people impact your technical team's work environment?
I try to impact theirs. The above is not wishy-washy. It is not focused on making everyone happy. It is focused on people acting as problem solvers and being tough on each other, while not getting dogged down on specifics to the extent long term interests are ignored.
Source: Experience and reading. Do read 'Getting to Yes', a seminal book (for me) and try some negotiation exercises with the team. Alternate who plays the trainer. Awesome learnings within.