I have the same problem but found a workaround for at least WP8.1 user. I'm able to select files via the file picker app "files" by Microsoft. Sometimes the playback start right after selecting the file, sometimes I have to wait a few seconds and sometimes I have to restart MoliPlayer. After restarting MoliPlayer the file is show inside MoliPlayer, too.
Sent from my Windows Phone using Tapatalk