You have some strange things going on at the top of your file. Comments interspersed:

my $words_file = @ARGV;

# Evaluating an array in scalar context returns the length
# of the array.  So if you are passing your script one filename,
# $words_file will equal '1', not the first argument from the 
# command line.  Pass it two filenames, and it will equal 2, etc.  
# But that doesn't matter, because of another bug:

open (my $fh, ">", $words_file);

# Here you open the file for writing, but never use it.
# (You should also check for errors, or use autodie.)

my @words;
while (<>) {
    push(@words, $_);
}

# Which turns out also not to matter, because you then use 
# the <> operator, which reads from the files in @ARGV 
# automagically.  So lines 4 & 5 (the first two I quoted), 
# though broken, don't affect anything else, and could be 
# discarded.
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