Just gutal or (for better understanding) Mongol gutal [u = oo]
What wrestlers wear were (and in some areas still are) the traditional everyday boots of the Mongolians. The word for them was gutal. They didn't have shoes. When Western shoes were introduced in Mongolia, the Mongolians called also them gutal. If you go in a shop in Mongolia and ask for gutal, they will offer you shoes. To get what wrestlers wear, you must say Mongol gutal.
One important shopping tip for you:
The Mongol gutals for wrestling don't differ in their form from the everyday Mongol gutals, but they have two additional things which don't belong to the everyday gutals: strings which are to be bound around each boot: one around the low part (blue pointer), one in the middle (green) which has a decorated oval piece of leather (red) to hold the string stable.
Don't forget to buy these special accessories when shopping!