Custom Post Type

You can use wp_get_post_terms() to pull the terms.

$taxonomy = 'project-category';
$terms = wp_get_post_terms( $post->ID, $taxonomy); 
var_dump($terms);

wp_get_post_terms() will return an array of terms because multiple terms may be assigned to a single post. This means that you will potentially get a set of terms, not just one, so you will need to choose which to use. That is, the first terms? The last term? The first would be $terms[0]->slug for example. This would be the case for your “pattern” here:

'post_type' => 'project',
'project-category' => 'Print',

You can alternately use a tax_query as found in the Codex:

    array(
        'taxonomy' => 'project-category',
        'field'    => 'term_id',
        'terms'    => array( 103, 115, 206 ),
    ),

Which in your case would look like:

$taxonomy = 'project-category';
$terms = wp_get_post_terms( $post->ID, $taxonomy,array("fields" => "ids")); 

  $query_args = array(
    'post_type' => 'project',
    'tax_query' => array(
        array(
          'taxonomy' => 'project-category',
          'field'    => 'term_id',
          'terms'    => $terms,
        )
    ),
    'posts_per_page' => 2
);