The problem could be that wperl doesn't have a console. You could try prefixing the command line with cmd.exe /c ..., or even start /wait /b ....

run ['cmd.exe', '/c', $program, $type], \$dot, ">", binary(), $out;
# or
run ['start', '/wait', '/b', $program, $type], \$dot, ">", binary(), $
+out;
[download]

I don't have GraphViz to test these.

Failing that, it would be relatively easy to replace the call to IPC::Run::run() with a call to piped open supplying the input ($dot) to the command via echo. Something along the lines of (untested):

sub _as_generic {
    my($self, $type, $dot, $output) = @_;

    my $program = $self->{LAYOUT};
    my $buffer;
    if ( ref $output || UNIVERSAL::isa(\$output, 'GLOB') ) {
        # $output is a filehandle or a scalar reference or something.
        # have to take a reference to a bare filehandle or run will
        # complain       
        my $out = ref $output ? $output : \$output;
        my $pid = open my $pipe, '-|', qq[ echo $dot | $program $type 
+] 
             or die $!;
        binmode $pipe;
        print $out <$pipe>;
        return;

    } elsif (defined $output) {
        # if it's defined it must be a filename so we'll write to it.
        system qq[ echo $dot | $program $type > $output ] ;
        return;

    } else {
        # but otherwise we capture output in a scalar
        my $pid = open my $pipe, '-|', qq[ echo $dot | $program $type 
+] 
            or die $!;
        binmode $pipe;
        return do{ local $/; <$pipe> };
    }
}
[download]

And that could be rationalised a bit.