The way you did it is pretty much the standard way to bubble exceptions up the stack. Basically something like:

function a(){ 
    throw new Exception("Exceptional!"); 
}

function b(){
    try{
        a();
    } catch (Exception $e){
        throw $e;
    }
} 

try{
    b();
} catch (Exception $e){
    echo $e->getMessage();
}

This will output:

Exceptional!

Do note that if you in b() do throw new Exception($e), you'll get:

exception 'Exception' with message 'Exceptional!' in sandboxed.php:1 
Stack trace: 
    #0 php(5): a() 
    #1 php(12): b() 
    #2 {main}

For your code however, you'd have to make sure that you are your try/catch block is within another try/catch block, otherwise you will end up with an uncaught exception error.

try{
    try {
        $ffprobe      = FFProbe::create();
        $streams      = $ffprobe->streams($infile);
        $videoStreams = $streams->videos();
        $audioStreams = $streams->audios();

        if (!$videoStreams) {
            throw new Exception("Could not find a video stream for file: " . $infile . PHP_EOL);
        }

    } catch (RuntimeException $e) {
        throw $e;
    }
} catch (Exception $e){
    echo $e->getMessage();
}

May I ask why you are bubbling exceptions like this rather than erroring out on a caught exception?