No. Mongolia doesn't ask visitors to fill in an online arrival form (also called an entry form, immigration card or landing card) before they travel. Independent travellers must register with the Immigration Agency after arrival. Some nationalities need an eVisa.
Do I still need a visa for Mongolia?
An arrival form is not a visa. Whether you need a visa or an electronic travel authorization depends on your nationality, so check Mongolia's official immigration website or your own government's travel advice.