Classical Mongolian is actually not a straightforward 1-to-1 conversion, and it's not clear if Khalkha Mongolian and Classical Mongolian should be treated as the same language in Google (Classical Mongolian is a common writing language not just for Khalkha Mongolian used in Mongolia, but also for Buryat and, but in Cyrillic those two languages are written differently).

E.g. the first line of a poem from linguamongolia.com, "saiqan časutu čağan ağulan-dur" (see http://www.linguamongolia.com/reso1.html , White Mountains document for original script) would be written "сайхан цаст цагаан уулд" (saihan cast cağan uuld) in Khalkha Mongolian orthography, if I'm not mistaken.

But then, sometimes Google Translate is happily combining two languages. E.g. it can translate from Crimean Tatar, but it will detect it as Tatar, even though it's a different language...

But it actually is "Mongolian - Cyrillic".

It's simply mislabeled (or not clearly labeled, whatever you call it).