The footage, posted online by human rights activists, showed soldiers applying a burning stick to the genitals of one of the unarmed men and threatening another with a knife.
The hearing, in the provincial capital Jayapura, comes ahead of a visit by US President Barack Obama to Indonesia. In July the Pentagon announced that it would resume ties with the country's special forces.
The video drew international attention to allegations of widespread killings, torture and abuse of activists and civilians in restive Maluku islands.
Three low-ranking troopers appeared in the morning - Second Private Syaminan Lubis, Second Private Joko Sulistyo and Second Private Dwi Purwanto from the 753 Arga Viratama infantry unit based in Nabire, Papua province.
Two other soldiers were called to appear as witnesses. One of them, a lieutenant, appeared separately as a defendant in the afternoon.
The military refused to answer questions about the case.
The four soldiers have been charged with disobeying orders, according to the indictments read in court. There was no mention of any charges relating to the alleged physical abuse of the two civilians, although the government has admitted that its troops were responsible for the torture.
The Sydney Morning Herald newspaper, which reported the existence of the video , quoted one of the victims as saying the torture went on for days.
Victims Tunaliwor Kiwo and Telangga Gire are in hiding, fearing reprisals from the Indonesians.
President Susilo Bambang Yudhoyono said Monday there was "no immunity" for members of the country's armed forces, before meeting Australian Prime Minister Julia Gillard in Jakarta.
Indonesia incorporated the resource-rich but desperately poor western half of the New Guinea island in the 1960s after a UN-backed tribal vote. But separatists, some of whom have formed armed groups, claim the poll was a sham and say that the military has committed multiple atrocities in the province.