On Wikipedia (awesome source I know) it says
'The nomads on the countryside are self-supporting by principle. Travellers will find yurts marked as "guanz" in regular intervals near the roadside, which operate as simple restaurants. In the yurt, which is a portable dwelling structure, Mongolians usually cook in a cast-iron or aluminium pot on a small stove, using wood or dried animal dung (argal) as fuel.'
'The most surprising cooking method is only used on special occasions. In this case, the meat (often together with vegetables) gets cooked with the help of stones, which have been preheated in a fire. This either happens with chunks of mutton in a sealed milk can ("Khorkhog"), or within the abdominal cavity of a deboned goat or marmot ("Boodog").'
It does not say that they eat the Marmots, just that they use them to cook in on special occasions. Could the Mongolian use his Yurt as a restaurant and needs it for that, which could be shown simply by a sign on it, or is he just mega hungry and has no sheep to eat?
Just found this at http://mongoluls.net/ger/meatmilk.shtml:
'The meat-dependent diet arises from the need for hearty food to stave off the cold and long winters. Traditionally nomadic herders, Mongolians have for centuries been dependent on mostly animal products for their dietary staples. Now after over nine years of transition, the traditional diet has been used as a shield against hunger and for the wealthy, subject to the influence of imported foreign foods and cuisine. When the Russians pulled the plug on Mongolia's aid in 1991, the economy went into a severe crisis. For many Mongolians it was their first experience of serious hunger. The staple traditional diet of meat, milk and flour saw many people through this crisis, when food imports from the former Soviet Union dropped off.'
This could give us a more recent timescale for when the film takes place, during 1991-92 during their economic crisis. This would account for why the Mongol is so hungry.