How can I implode an array while skipping empty array items?

How you should implement you filter only depends on what you see as "empty".

function my_filter($item)
{
    return !empty($item); // Will discard 0, 0.0, '0', '', NULL, array() of FALSE
    // Or...
    return !is_null($item); // Will only discard NULL
    // or...
    return $item != "" && $item !== NULL; // Discards empty strings and NULL
    // or... whatever test you feel like doing
}

function my_join($array)
{
    return implode('-',array_filter($array,"my_filter"));
} 

To remove null, false, empty string but preserve 0, etc. use func. 'strlen'

$arr = [null, false, "", 0, "0", "1", "2", "false"];
print_r(array_filter($arr, 'strlen'));

will output:

//Array ( [3] => 0 [4] => 0 [5] => 1 [6] => 2 [7] => false )

You can use array_filter():

If no callback is supplied, all entries of input equal to FALSE (see converting to boolean) will be removed.

implode('-', array_filter($array));

Obviously this will not work if you have 0 (or any other value that evaluates to false) in your array and you want to keep it. But then you can provide your own callback function.

I suppose you can't consider it built in (because the function is running with a user defined function), but you could always use array_filter.
Something like:

function rempty ($var)
{
    return !($var == "" || $var == null);
}
$string = implode('-',array_filter($array, 'rempty'));