The 1980 Summer Olympics was held in Moscow, Soviet Union.
Many countries boycotted the games initiated by the United States for Soviet Union's invasion of Afghanistan.
But there were some communist countries in the boycotting countries that I think wasn't related to the US-backed boycots; such as People's Republic of China, Albania (which had left-wing leaning at the time), and some else.
What was the reason for communist countries to boycot the 1980 games?
Sino-Soviet split has been already mentioned in the comments as an example of lack of homogeneity in the Communist camp, where some communist countries could side with western boycott for their own political reasons. The additional reason for China was the People's Republic of China recent accession to formal status as the sole representative of China (instead of the Republic of China=Taiwan), after boycotting the olympics altogether since 1956:
The Chinese Olympic Committee in its current form was recognized in 1979. Before the Chinese Civil War, athletes competed as the Republic of China (ROC) at the Olympics. The ROC continued to compete from 1952 (Summer Olympics) to 1976 (Winter Olympics), but only representing athletes from the island of Taiwan (although the football team members of ROC in the 1960 Olympic Games were overwhelmingly Hong Kongers). The dispute over use of the name China resulted in the PRC boycotting the Games completely during these years. In 1979, the International Olympic Committee passed a resolution for the ROC team to be designated Chinese Taipei, and this opened the door for the PRC to finally join the Olympic movement.
In other words, good relationships with the West were one of the primary political objectives at that time.
In case of Albania one can cite similar Albanian-Soviet split, formally attributed to Khruschev abandoning real communism (i.e. Stalinism) and engaging in revisionism of Marx teaching, although the real reason was likely the Soviet Reapproachment with Yugoslavia (Albania's hostile neighbor, who similarly was in a state of split with the USSR - see Tito-Stalin split.)
Update
From Playing Games between the superpowers : the People's Republic of China's participation in the 1980 and 1984 Olympic Games by Xiaowei Yu:
There are several reasons for China’s boycott of the Moscow Olympic Games. Based on the comments of Wu Shouzhang, the Vice- President of the COC in the 1980s,
[in 1979] Soviet-supported Vietnam military forces put much stress on Chinese southern border and Soviet military forces threatened Chinese northern border for a long time, while the Soviet invasion of Afghanistan resulted in that Chinese western border was also directly threatened by Soviet military forces. Under this situation, China was besieged by the Soviet Union’s military forces. Therefore, the [PRC] government must take actions to break the siege. The boycott of Moscow Olympic Games was an efficient way to express our protest and attitude.
He also stated that although the Chinese athletes were performing poorly at the time, they had a strong desire to compete for their country. Therefore, he denied that the boycott was because of the Chinese athletes’ low-level performance. Wang Dinghua has the same opinion in respect to this point. He argues that the possibility that China gave up the Moscow Olympic Games because of the poor athletic performance of its athletes did not exist. Additionally, Pei Dongguang, a professor of Olympic Studies at the Capital Institute of Physical Education, expressed the same opinion. He commented that prior to 1980 the Chinese athletes had not competed in the Olympic Games for a significant period and they had not achieved any Olympic medals. Attending the Olympic Games following the reinstatement symbolized more political meanings rather than the athletic meanings of Chinese national sport. Therefore, he stated, it is improbable that China’s boycott was due to the poor athletic performance of its athletes at the time. Pei Dongguang stated another possible reason for the boycott. Based on his comments, Sino-Soviet relations was not au pair; the Soviet Union always tried to dominate China while China resisted these efforts by the Soviet Union. The boycott expressed an attitude that the PRC government was not influenced or even controlled by the Soviet Union. Cui Lequan, the General Secretary of the Chinese Society of Sport History (CSSH), stated that between 1971 and 1979, the PRC government had been trying to improve the relationship with the USA. Following the normalization of Sino-US relations in 1979, a positive relationship had been dramatically developed. Both countries initiated a multi-aspect cooperation agreement between 1979 and 1980. The boycott expressed that the PRC government wanted to further develop Sino-US relations in the 1980s. In addition, taking the same actions as the USA could also attain the rapprochement from western countries, which was needed for the PRC’s restoration of international relations and domestic reconstruction. On the other hand, the Soviet Union invaded Afghanistan, a neighbor of China, which seriously threatened the PRC’s national security. Furthermore, in January 1980, Soviet leader Leonid Brezhnev threatened that they might destroy the Chinese nuclear base so that the USA would have to maintain the cooperative relationship with the Soviet Union instead of protecting its “Chinese friends.” Therefore, for the PRC, to boycott or not was a simple choice with a clear cause and effect. Chinese Vice-Premier Deng Xiaoping publicly stated in 1980 that the enhanced relationship with the USA would become a long-term national strategy of the PRC; in addition, according to Deng Xiaoping, it was suggested that the USA, Japan, Western European countries, and the PRC should create an alliance against the Soviet Union in the 1980s.
After Hungary in 1956 and Czechoslovakia in 1968, Afghanistan in late 1979 marked another instance of the Soviet Union invading countries ruled by communists.
Therefore it was natural for non-Soviet-aligned communist countries such as China or Albania to protest against such invasions, including by boycotting the olympics.
In the case of China, one should not forget that it was very friendly with Pakistan, which was directly affected by the events in Afghanistan. And Soviet support for Vietnam (which had invaded China-allied Cambodia in 1978 and in turn got invaded by China in 1979) may also have been somewhat relevant.
China had also condemned the Soviet invasion of Czechoslovakia in 1968, but not sure about Albania.
