I think -1c is correct.
The reason it wasn't playing the most recent video was because 30 seconds wasn't long enough of a delay for the video to begin downloading.
FILE=`/bin/ls -1t |head -1`
youtube-dl-x --no-part -f 5 -o "%(stitle)s.%(ext)s" `xclip -out` &
while [ "$FILE" = "`/bin/ls -1t |head -1`" ]; do sleep 5 ; done
mplayer `/bin/ls -1t |head -1`