Below I'll make some suggestion of how you could take advantage of some nice Perl 6 features, and write more idiomatic Perl 6 code:

my $filename = shift @*ARGS or die "You need to pass in a filename.";
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Instead I usually write

sub MAIN($filename) { 
    # rest of the mainline code here 
}
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The MAIN sub does the command line parsing for you, and also gives an automatic usage message.

rx/ \w+ [<punct> \w+]* /

This also be written as rx/ [\w+] ** <punct> /. Here ** is the general quantifier, a ** 4 matches 4 a's, a ** <punct> matches an arbitrary number of a's, separated by punctuation.

sub natural_cmp ($a, $b) {
    my ($first, $second) = ($a, $b);
    my ($one, $two) = ($first, $second).map({ .=subst(/(\d+)/, 
      -> $/{ sprintf( "%s%c%s", 0, $0.chars, $0) }, :g).lc });
    return ($one cmp $two);
}
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If you leave out the = in .=subst, no in-place modification takes place; instead the modified value is returned, and the original variable remains untouched.

So you can write

sub natural_cmp ($a, $b) {
    my ($one, $two) = ($a, $b).map(*.subst(/(\d+)/, 
      -> $/{ sprintf( "%s%c%s", 0, $0.chars, $0) }, :g).lc);
    return $one cmp $two;
}
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If you happen to need a copy, you can also say sub mysub($a is copy, $b is copy), so you don't need to come up with more variable names.