use strict;
use Data::Dumper;

chomp(my @files = <DATA>);

# find unique basenames
my @basenames = keys %{{ map { (split/\./)[0] => 1 } @files }};

# find unpaired files
foreach my $basename (@basenames) {
    my @matches = grep (/$basename/, @files);
    print "$matches[0]\n" if $#matches == 0;
}
[download]

No, this solution breaks if any filenames have regex-significant metachars, or are partially within a larger filename.

In my opinion, the original solution is actually the most direct, as this is a classic set difference problem.