meta_query to check all custom fields

Short of coming up with a MySQL query yourself, you could get a list of distinct meta_keys and build your query array based on the results.

On another note, I think you may have misunderstood the meaning of EXISTS. It doesn’t denote finding the value parameter passed within the value of the given meta. I think you actually mean LIKE, but please correct me if I’m wrong.

$query_arg = array(
    ...
);

global $wpdb;

$meta_keys = $wpdb->get_col("SELECT DISTINCT `meta_key` FROM {$wpdb->postmeta}");

foreach($meta_keys as $meta_key){
    $query_arg['meta_query'][] = array(
        'key' => $meta_key,
        'value' => 'mykeyword',
        'compare' => 'LIKE'
    );
}

$query_arg['relation'] = 'OR';

Although this is likely not the most optimised way of doing things, from a MySQL standpoint.