The OP requested not to include helloworld/ since there were subdirectories. This addition to your script works but will not be efficient for a large file with the nested searches.

use strict;
use warnings;
use File::Basename qw( fileparse );

my %seen;
while (<DATA>) {
    (undef, my $path) = fileparse( $_ );
    print "$path\n" unless $seen{$path}++;
}

print "="x70,"\n";

foreach my $key (keys %seen){
    print "$key\n" if 1 == scalar grep { /\Q$key/ } keys %seen;
}
__DATA__
testing123/
foobar/
helloworld/
helloworld/r1/
helloworld/r1/helloworld-5-0.noarch.rpm
helloworld/r1/testfile23.txt
helloworld/r1/tomcat-7.0.27.rpm
helloworld/r2/
helloworld/r2/helloworld-2-0.noarch.rpm
helloworld/r2/testfile12.txt
helloworld/r2/tomcat-5.0.52.rpm
hellotest/
[download]

For large files sorting and a pass to remove the current element if the next element matches is needed. Or, assuming that the original file is sorted just check each element against the next one.

use strict;
use warnings;
use File::Basename qw( fileparse );

my %seen;
my @directories;
while (<DATA>) {
    (undef, my $path) = fileparse( $_ );
    #push @directories, $path;  
    ## update, I indended to put the push inside the unless block.
    ## The original works but not exactly as I expected since it puts
    ## duplicates in the array. 
    #print "$path\n" unless $seen{$path}++;
    unless ($seen{$path}++) {
        print "$path\n";
        push @directories, $path;
    }
}

print "="x70,"\n";

foreach my $index (0..$#directories-1){
    my $current = $directories[$index];
    print "$current\n" if not $directories[$index+1] =~ /\Q$current/ ;
}
### assuming the last one is always terminal
print $directories[$#directories], "\n"; 
__DATA__
testing123/
foobar/
helloworld/
helloworld/r1/
helloworld/r1/helloworld-5-0.noarch.rpm
helloworld/r1/testfile23.txt
helloworld/r1/tomcat-7.0.27.rpm
helloworld/r2/
helloworld/r2/helloworld-2-0.noarch.rpm
helloworld/r2/testfile12.txt
helloworld/r2/tomcat-5.0.52.rpm
hellotest/
[download]

Update: This seems to work on a single pass through the file.

use strict;
use warnings;
use File::Basename qw( fileparse );

my $first='';
my $second='';

while (<DATA>) {
    $first = $second;
    (undef, $second) = fileparse( $_ );
    print "$second\n" if eof DATA;  
    next unless $first;
    unless ( $second =~ /\Q$first/) {
        print "$first\n";
    }
}


__DATA__
testing123/
foobar/
helloworld/
helloworld/r1/
helloworld/r1/helloworld-5-0.noarch.rpm
helloworld/r1/testfile23.txt
helloworld/r1/tomcat-7.0.27.rpm
helloworld/r2/
helloworld/r2/helloworld-2-0.noarch.rpm
helloworld/r2/testfile12.txt
helloworld/r2/tomcat-5.0.52.rpm
hellotest/test.txt
hellotest/
[download]