Sorry, I figured it out.
I moved the file from
wp-content/uploads/GeoIP/GeoLiteCity.dat
to
wp-content/uploads/GeoLiteCity.dat
and the plugin was able to find the file automatically.
But there are two issues here.
1. The error I got earlier is incorrect. The file is still within my WordPress install directory and should be accepted by the plugin (bug-fix)
2. I remember seeing somewhere in a screenshot where the path I originally set was shown. Hence I chose to store the file in a folder labeled GeoIP.