Although the United States and the Soviet Union did not directly engage each other in armed conflict, the hostility between the two powers spilled over to other countries. The two countries launched major campaigns to seek allies and spread their ideologies. The situation gave rise to proxy wars where members of the different countries were torn between siding with the United States or the Soviet Union. The tensions escalated in these countries, leading to full blown armed conflicts between these different groups, each with the support of a Cold War power. Thus, it is impossible to discuss the Cold War without acknowledging the proxy wars that led to the loss of lives for many around the world. For instance, both the United States and the Soviet Union supported different groups in the Chinese Civil War, which led to millions of casualties and deaths. Similar patterns were followed in Africa during the Portuguese Colonial War, the Congo Crisis, and the First Sudanese Civil War among other conflicts in Asia and the Middle East.

As you say, the Cold War was not an actual war, but there was plenty of actual violence that happened during the Cold War because of the tensions between communism and the West.

To take a large example, the Korean War happened because of the Cold War.  More than 36,000 Americans died in that war, not to mention hundreds of thousands of Chinese and Koreans.

But there were also smaller numbers of people killed in lesser encounters during the Cold War.  One example of this was Major Rudolf Anderson who was killed when the U-2 spy plane he was flying on a mission over Cuba was shot down during the Cuban Missile Crisis.  There were many other small-scale incidents like this.

So, while the Cold War itself was not a shooting war, there were plenty of people who got killed as a result of the tensions.