Assuming you're not hanging on to old versions of Perl, I'd write it as:

given ($_) {
    when (/filename\s*=\s*(\S+)/) {$file = basename($1)}
    when (/go/ && exists $files{$file}) {
        push @PLACE, @batch;
        delete $files{$file}
}
@batch = ();
[download]

If it's in a for loop, and $_ is your loop variant, you can even omit the given.

Thing is, I think I understand what is happening here but not why: essentially, the call to basename() is not finding a good value in $1, which should have been returned from the match by the (\S+).

But you're not matching. qr// creates a pattern, it does not perform a match. qr/filename\s*=\s*(\S+)/ is always true. If you want to match, use m// instead.