Like many other countries, rice is pretty common and fairly cheap, so Mongolians do eat rice. However, it is not the staple dish or the main ingredient in Mongolian homes. East Asian countries on the other consume more rice than Mongolians.
Meats and dairy are more heavily consumed in Mongolian households, which might explain the bulkier and broader build that Mongolians generally tend to have. However, there are plenty of Mongolian dishes that have rice such as Plov or Budaatai Khuurga, Budaatai shul or Rice Soup, etc.
In conclusion, while rice is consumed generally, it’s not the main staple ingredient for Mongolian diet.