Their army size and military spending is a fraction of Russia’s, plus economic ties and nukes existing. Although now would be probably one of the best times to go against Russia militarily, since they’re stretched pretty thin at the moment, I doubt Mongolia would be the one to do it.
There are a lot of economic ties between Mongolia and Russia. You don’t get a lot of options when you’re landlocked and sandwiched between two large powers. So, Putin has a fair amount of leverage there, more than in most places.