That's pretty much it. I assumed it has to do something with how the Hangul are represented in Latin letters, but the corresponding Wiki page didn't have any part of "eogksalsrnr" in the row where "Korea" comes up, so I guess it's not quite that. Anyone know something about this?
The correspondence between "eogksalsrnr" and "대한민국" is based on the standard Korean keyboard layout. E is on the same key as ㄷ, O is on the same key as ㅐ, etc.
Google probably thinks you have a Korean keyboard that is accidentally in English mode.
It is not limited to Korean language. If you search for English words that have no meaning in English, Google will search for probable words in other languages with those characters in standard keyboard of that language. I have seen some Koreans just search in English but with right characters in Korean and get sensible results.