map { $_ ? $_ : () }
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means (if we pretend that there's a built-in function is_true()) the same as:

map {
  if (is_true($_)) {
    $_;
  }
  else {
    ();
  }
}
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In Perl, there are five things that are considered false: undef, the empty string, the number zero (including when written 0e0, 0.0, etc), the string "0" (but not strings like "0e0" or "0.0") and objects which overload conversion to boolean to return false.

The zeros passing through your map are false, thus go down the "else" path.

So we don't want to test is_true; we want to test whether each string has any characters... i.e. a non-zero length:

map { length($_) ? $_ : () }
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Any any map which ends with ?$_:() should probably be a grep:

grep { length($_) }
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Thanks for your thought out reply. Writing in Perl is becoming much easier thanks to you!