While there is room for quibbling about the meaning of "set up", if we're flexible with that term, they most certainly set up a communist government after overthrowing the Khmer Rouge government.

The Kampuchean United Front for National Salvation (AKA the Salvation Front) was founded by the Kampuchean People's Revolutionary Party (KPRP), which was the oldest major Cambodian communist part. The KPRP had roots in the Indochinese Communist Party (ICP), founded in 1930, which was a communist independence movement. The ICP was built on a core of the Vietnamese Communist Party (VCP), which in turn formed from a 1930 merger of the northern and southern Vietnamese communist parties, the Communist Party of Indochina and the Communist Party of Annam respectively. Cominterm wanted the VCP to cover all of Indochina, so they broadened to cover Cambodia and Laos and renamed themselves the ICP. The ICP dissolved itself in November 1945, after the Việt Minh had proclaimed the Democratic Republic of Vietnam on 2nd September 1945, and were fighting for independence. In 1951, the former Cambodian section of the ICP founded the KPRP (and the Vietnamese section the Workers' Party of Vietnam (which is now the ruling Communist Party of Vietnam) and in 1955, the Laotian section founded the Lao People's Party).

The KPRP formed a party to run in the Cambodian elections of 1955: the People's Party. The People's Party became the Workers' Party of Kampuchea (WPK) in 1960, and then the Communist Party of Kampuchea (CPK) in 1966. The CPK became known as the Khmer Rouge. As Khmer Rouge members fled (mostly to Vietnam) to escape purges and execution, they reformed the KPRP as a moderate communist party alternative to the extreme nationalism of the Khmer Rouge under Pol Pot. To present a broad-based opposition front to the public, the KPRP formed the Salvation front, which included non-communists (e.g., Buddhist clergy). However, the leadership of the Salvation Front was dominated by the KPRP leadership.

As Vietnam pushed aside the Khmer Rouge in the invasion, the Salvation Front formed a provisional government, the Kampuchean People's Revolutionary Council (KPRC), dominated by the KPRP just as the Salvation Front itself was. The top leadership of the KPRC were all former Khmer Rouge members: Heng Samrin had been a division commander in the Khmer Rouge army, Chea Sim was also a military commander, Pen Sovan had worked in propaganda, and Chan Sy had been a prominent communist leader who collided with Pol Pot's faction in 1973 and fled. Hun Sen, the long-term future leader of Cambodia, had been a batallion commander in the Khmer Rouge. The KPRP, the Salvation Front, and the KPRC were pro-Vietnamese and anti-Khmer Rouge, which suited Vietnamese aims, and Vietnam let the KPRC administer the new Cambodian state, while Vietnam supported them by their military occupation. The KPRC proclaimed the new state, under the name of the People's Republic of Kampuchea. The KPRC remained as the official government until 1981, when a new constitution was adopted; the new Council of Ministers was just as strongly communist, since the KPRP was the ruling party in a on-party state.

The People's Republic of Kampuchea was renamed the State of Cambodia in 1989, but remained a on-party state under the control of the KPRP. In 1991, as part of the ongoing peace process, the KPRP officially dropped its Marxist-Leninist ideology, and became the Cambodian People's Party (CPP). 1991 also saw steps towards free elections, to be held in 1993. In 1992, the United Nations Transitional Authority in Cambodia (UNTAC) took the reins of government in order to hold the elections. In 1993, the state became the Kingdom of Cambodia, with Norodom Sihanouk as King and head of state, and power in the hands of the elected government, thoroughly dominated by the CPP under Hun Sen. While the CPP is no longer communist, the former leadership of the KPRP continues to lead the CPP (except for attrition due to old age and ill health). While Cambodia is no longer officially a one-party state, the CPP is electorally-dominant to a most remarkable degree: they current hold all 125 seats in the National Assembly, and 58 of 62 seats in the Senate. Their worst electoral performance since their suppression of their more popular royalist opposition party, the National United Front for an Independent, Neutral, Peaceful and Cooperative Cambodia (FUNCINPEC) and Hun Sen's overthrow of his co-premier Norodom Ranariddh (a son of Norodom Sihanouk) in the 1997 coup was in the 1998 elections, gaining only 64 of the 123 seats in the National Assembly. (Previously, FUNCINPEC had won more votes and seats than the CPP, but the CPP refused to give up power and forced FUNCINPEC to rule in coalition with them - such are the wonders of Cambodian politics.)

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!