What Buddhist principle is Siddhartha demonstrating in the passage "...Kamaswami could never persuade his colleague [Sid] that it served any purpose to utter troubled or angry words, to form wrinkles on the forehead and sleep badly."
To understand this passage you have to first understand the Nobel Eight-Fold Path. After Buddha had discovered all of the sadness and suffering in the world he set out to try to figure out how to end said sadness. Through this he constructs the four noble truths, the final truth being that to end all of pain and suffering one must follow the eight-fold path.
The eight-fold path is broken into three aspects: Wisdom, Virtue, and Concentration. This quote speaks to the first step within Virtue, which simply put is known as having the "right speech" or Samma Vaca.
People traditionally look at Right Speech as meaning "don't say anything mean," or as the quote says, "troubled or angry words," but it actually has a deeper meaning, as many stricter Buddhists have taken it to mean literally no talking. One must ask what the point of the words that you are saying is, and whether they are actually necessary.
Whether they be troubled words or words at all, this quote is speaking to that idea.