SOUTH YEMEN is a small, poor, back-of-beyond place. But it happens to have a sensitive location at the tip of the Arabian peninsula and a good harbor at Aden. These assets, along with its Marxist government and Soviet patronage, give the People's Democratic Republic of Yemen an evident strategic potential. Certainly the Kremlin has been attentive to it; in recent years it has invested considerable effort in consolidating the local power structure, the only Arab Marxist regime.

The effort, however, has gone poorly, or so one must judge by the current upheaval in South Yemen. A former president, it seems, attempted a coup against the incumbent, who'd earlier forced him out. A violent struggle, not easily followed from the outside, has been going on. Besides the personal aspect of the struggle, there is evidently a tribal aspect, as there tends to be in the Yemens (the other one is North Yemen). The conflict may also have a policy aspect. The challenger criticizes the incumbent for trying to "link the country with the wheels of neocolonialism and reactionary influence." Translation: the incumbent had moved toward some calmness with South Yemen's conservative neighbors on the Arabian peninsula, including Saudi Arabia and Oman as well as North Yemen, and had opened the country a bit to Western economic contacts.

In brief, the label Marxist is bestowed on both factions but the incumbent seems more of the go- slow sort, while the challenger is the fellow whose contributions to the subversion of North Yemen and Oman troubled the Carter administration considerably in 1979.

Some glee is being taken at the spectacle of the Kremlin's evident embarrassment. Its followers are shooting it out and it has had to evacuate some number of the several thousand resident Soviet-bloc personnel. Its attempt to settle things down have so far been in vain. The Soviet purpose, however, is unclear. Earlier the Soviet mission in Aden appeared to be assuming a peacemaker's role. Now it is reported that Moscow has taken the rebels' side and may even have men with the rebel forces in the street.

So there is no real comfort for the West in the latest turbulence, and certainly no visible gain for the people of South Yemen. Whatever the differences between the contending factions, a readiness to defer to Moscow remains the condition of a Marxist's holding power there. As elsewhere in the Marxist world, the people are not consulted. Casualties are reported to be in the thousands, and rising.