To quote the great William C. Johnstone, writing in his 1962 article "The Appeals of Communism in Asia," in The Annals of the American Academy of Political and Social Science, Vol. 342: American Foreign Policy Challenged,
Assessment of the appeals of communism in Asia is handicapped by false conceptions and generalizations about the peoples of South and Southeast Asia. In Western writings and in the Western press, they are identified as "Asians," although they do not accept this identification themselves. Communist appeals are directed at the ethnic-linguistic groups within each state.
So, to understand the appeals of communism to different groups in SEAsia we have to look at each group individually.
In Vietnam, the Communist faction emerged into WW2 in small number, but united under Ho Chi Minh's leadership. They had founded the Viet Minh, ostensibly a patriotic umbrella armed organization but in reality dominated by communists. Taking advantage of the chaos toward the closing of WW2, they emerged as the poor farmers' champion by establishing their own brand of communism with Indochinese elements, and fought on behalf of poor farmers against land owning families. They were politically strongest in the north, and weakest in the south, where a large number of patriotic groups vied for control. This is not to say they were very popular in the North, rather that they were able to consolidate their political power using both violent and non-violent means.
Over the course of the "Vietnam War" the South Vietnam government ended up being very unpopular due to a wide range of reasons that I won't repeat here. Between their failure to build security and provide economic help when needed, corruption, fighting between various factions, suppression of Buddhism, the South Vietnam government ended up being seen as a government that taketh but never giveth.
In Burma, unlike in Vietnam, the Communist factions emerged from WW2 into splinter groups ranging a rather wide spectrum. In terms of degree of appeal I do not know, but this splintering led to weakness.
In then-Malaya, the Communist party was strongly associated with the ethnic Chinese, and strongly collaborated with Mao's Communist Party of China. Poor rural Chinese farmers and miners comprised their strongest group of supporters, with the Malayan Communist party organizing strikes, and over WW2 led insurgencies against the Japanese. In turn, the Japanese violently reacted against Chinese communities, turning even more of them into the Communist party. The Japanese also arrested and killed many civilian leaders of the party, so the closing of WW2 saw a party that was dominated by military leaders in the rural areas. Further, their armed groups took control of Japanese armaments prior with some backing from the Allies. Most of these weapons were surrendered at de-mobilization but some were kept in the hands of party groups. This period saw a Malaya beset with economic problems, as they had had an export-oriented economy that was severely disrupted by WW2. Yet, the British were not able to address this challenge due to their own weakness in Europe. This turned the Communists against the British, and by 1948 they were able to gain sufficient popular support to launch military raids. This led to the Malayan Emergency that lasted until 1960. It failed due to their inability to influence the greater population outside their specific rural and largely ethnic Chinese supporters.
In Indonesia, Sukarno co-opted Communism into his brand of Nasakom: Nationalism, Religion, and Communism. The Communist party itself was quite popular, especially in rural areas and among trade unions, and by the 1960s it had 3 million members. But so were opposition against them. They had launched several abortive "revolutions" that made them suspect not only to other rival Republican and Islamist parties but also to Sukarno.
The Communist party saw Sukarno as a means of greater control and supported his switch to rule using Guided Democracy, and went along with his anti-imperialist, anti-colonialist rhetoric. This includes calls to invasion of West Papua (still withheld by the Dutch but claimed by Sukarno), and his anti-US stance due to US support of rebellions in Sumatra and Sulawesi. So western support of regional rebellions strengthened the Communist party.
The 1960s saw Sukarno strongly opposing the formation of the Federation of Malaysia as an independent nation, citing the legend of Majapahit to justify his rhetoric. Of course, this period saw the demise of both Sukarno and the Communist party as Suharto took control and suppressed Communism in Indonesia. There was an alleged failed attempt at a Communist coup led by some segments of the Presidential Guards, in an Era of tension that saw the Communist Party form armed militia. But if Roosa's book is to be believed, not all leaders supported this attempt nor are all of them informed. This became their downfall as they failed to mobilize; the nationalist faction in the army took control of government and the Communists ended up being eradicated.
So, what did Communism mean to them and what are the appeals? It was a mix of nationalism, economic opportunity, security in various meanings; it depends on whom you are speaking of.
Want to know more? Check out Benedict Anderson's The Spectre of Comparisons for a good perspective on nationalism in SEAsia; Frey/Pruseen's The Transformation of SE Asia: International Perspectives on Decolonization on how the aftermath of WW2 and subsequent independence movements factored into this; Jeffrey's Asia: The Winning of Independence for more on the same.