I can answer the first part of your question (how this form of government came into being) but don't have the expertise to answer the second part (how was it ideologically justified).

First, some context.

Grenada, pre-revolution, had a Westminster style of government. This meant that the head of government was a Prime Minister who could command the confidence of Parliament and the head of state was Queen Elizabeth II (via her Governor-General who, while appointed by her, was selected by the Prime Minister). On paper, the Queen/Governor-General had immense power, but practically acted as a rubber-stamp.

Sir Eric Gairy and his party had ruled Grenada since independence. In the 1976 an anti-Gairy coalition secured almost half the vote. The main party in this coalition was the New Jewel Movement. Maurice Bishop of the NJM became the leader of the opposition.

On March 13, 1979, the NJM overthrew Gairy's government in a nearly bloodless coup. Gairy had become increasingly unhinged, corrupt and unpopular and there was widespread popular support for the coup. Bishop had a strong pragmatic side and was well aware of the need to maintain relations with the west as well as assure the populace that change going forward would not be radical.

Accordingly, on the day of the coup, Bishop told the populace that democratic freedoms would be restored. When the People's Revolutionary Government was formed on the 16th, it included representatives from the conservative opposition party as well as moderate businessmen. Bishop became the Prime Minister and the existing Governor General remained in office. The new government affirmed its commitment to constitutional government.

The strategy worked and western governments and Grenada's neighbours recognized the new government.

Shortly after, on the 25th, Bishop promulgated a series of so-called People's Laws which suspended the constitution (while noting that there would be a "return to constitutional rule at an early opportunity") and limited the powers of the Governor General (while reaffirming the role of the Queen as head of state). However, while this was certainly a move towards communist dictatorship just as Augustus kept the trappings of the Roman Republic so to did Bishop keep the trappings of the Westminister style of government. The PRG saw keeping the Queen as especially helpful with maintaining good relationships with the UK and Canada (both which had a close connection to Grenada). While Bishop railed against the United States, he also knew not to poke the bear too hard - especially after the election of strongly anti-communist Ronald Reagan.

Note that Bishop did not have absolute power within the PRG or the NJM. While he represented a more populist approach, his Deputy Prime Minister Winston Coard was a more ideological and doctrinarial Marxist. Over the four years of Bishop's rule, Coard became more and more concerned that Bishop was too ideologically adrift. On October 16, 1983, Coard overthrew and murdered Bishop. Widespread popular unrest occurred and shortly thereafter, the United States invaded and the PRG experiment was ended.

As noted, I cannot comment on the ideological justification for retaining the monarchy. However, as I set out above the decision was made for practical, not ideological, reasons.