Communication skill is a supreme skill for any person. It is like a server without the network drivers which still has network interface controller but not using it efficiently.

Communication allows us to achieve our goals, to ask for something, to make sure other person understood what we really wanted to say and it is not so easy.

Moreover, communication allows us to go outside of human designed systems which might have "bugs". For example, you are in cafe which offers you a a lunch with coffee or tea for 5$. You can ask for water instead of tea or coffee but if you are hesitated to do so you are limited to the system itself always.

For most developers it doesn't mean you should be an expert, but you should be able just to talk, to tell your arguments to other team members and managers, to ask for help, opinion.

For sr. engineers and especially for engineering managers, tech leads, architects, CTOs communication is a critical skill.

Yes! It plays a major role. Communication skills are very much required to put forward your views and actively participate in a discussion, especially brainstorming sessions.

I would like to answer this in the context of non-English speakers to show its importance.

Communication for these guys is split into two parts. All the vocal and visual expressions one side and their English on the other.

Even though they are smart and voluble, when it comes to conversing in English, they surely have hiccups. Most of the times, they face hard times to put forward their point to fellow english speaking programmers as well as to actively participate in any discussion. Many people dont even utter a word because of the fear of sounding awkward.

So, ability to converse in the language plays a major role when there are people from diversified backgrounds.