How about this then?

#!/usr/bin/perl

use 5.18.3;
use warnings;

chomp (my @words = <DATA>);
my %cnt = map { $_ => 0 } @words;

foreach my $tf (glob "*.log") {
    printf STDERR " %-40s\r", $tf;
    open my $fh, "<", $tf or next;
    while (<$fh>) {
        $cnt{$_}++ for grep { exists $cnt{$_} } m/(\w+)/g;
        }
    }

printf "%-20s : %6d\n", $_, $cnt{$_} for sort { $cnt{$b} <=> $cnt{$a} 
+} @words;
__END__
tux
dromedary
camel
dream
milk
druid
monk
wizard
azaghal
perl
[download]

I was more wondering about case sensitiveness

I timed that against the original approach. My code (with 8 words): 19 seconds, OP code: 57 seconds. That difference will exponentially grow with the number of words: with 23 words 20 seconds versus 175 seconds. Total text size was 273 Mb.