User Without Email?

It’s possible, just not so easily via the Users page without some hackery.

The WordPress Function wp_create_user will let you insert users without email addresses, so a little custom plugin to accept a login name and password, and a call to wp_insert_user or wp_update_user should work for you. Unfortunately I don’t have time to code it up for you, but perhaps this will point you in a direction.

$userdata = array ('user_login' => 'someuser', 'user_pass' => 'swordfish');
$new_user_id = wp_update_user( $userdata );

Update for people looking for a solution with the REST-API:
Unfortunately, this is not possible by the rest-api. the email is required there. see: https://developer.wordpress.org/rest-api/reference/users/#create-a-user