Backup software for backing up specific files only
Your Mac has batteries already included. The only drawback (for some people) than it is command line (Terminal.app) solution.

The following shell script can do the job

case $# in
    (2) SRC="$1"; DEST="$2";;
    (*) echo "Usage: $0 source destination"; exit 1;;
esac

cd "$SRC" || exit 2
find . -type f -print0 | grep -ziv 'cpan' | grep -ziE '.(avi|mov|mp4)$' | rsync -n -av0 --files-from=- ./ "$DEST"


Save it into some file (e.g. mybackup.sh) and run from the terminal: sh ./mybackup.sh /path/to/the/source /path/to/the/dest, e.g.:

sh ./mybackup.sh ~/Downloads /Volumes/your_usb_hdd_name/path


Run the scipt and if you satisfiled with the result (will print out what will backing up), remove the '-n'. (The '-n' mean dry run)

rsync can do network backup to, or is possible emulate the TimeMachne functionality too, (incremental backup), etc - rsync is extremely powerful.

If you interested, can learn more with man rsync from the Terminal.

Ps:
Or, it is not enough simply select in finder's search "All Movies" and simple drag&amp;drop to result into the destination?