Can’t sort custom post type by random

You could use meta_query to search in the meta data, and then sort them as random:

$args = array(
        'posts_per_page' => 4,  
        'post_type' => 'projekte', 
        'orderby'=> 'rand',
        'post__not_in' => array( get_the_ID() ),
        'meta_query' => array(
            array(
                'key' => 'ecpt_skills',
                'value' => $projektart,
                'compare' => 'LIKE',
            )
        ),
    );

There is also a mistype in your code, the post__not_in should be written as 'post__not_in'.

And also, if your meta value is not numeric, you should use meta_value instead of meta_value_num.