Modules can now store settings for node types using the new ThirdPartySettingsInterface

In Drupal 7, modules could implement hook_form_node_type_form_alter(), add form elements and they were automatically saved as variables with a $node_type->type suffix.

In Drupal 8, they can use ThirdPartySettingsInterface to store settings, but need to provide a #entity_builders callback to control which values are saved.

7.x

function menu_form_node_type_form_alter(&$form, $form_state) {
  $type = $form['#node_type'];
  $form['menu']['menu_options'] = array(
    '#type' => 'checkboxes',
    '#title' => t('Available menus'),
    '#default_value' => variable_get('menu_options_' . $type->type, array('main-menu')),
    '#options' => $menu_options,
    '#description' => t('The menus available to place links in for this content type.'),
  );
}

// Then the setting can be used as:
$menu_options = variable_get('menu_options_' . $type->type, array('main-menu'));

8.x

function menu_ui_form_node_type_form_alter(&$form, FormStateInterface $form_state) {
  /** @var \Drupal\node\NodeTypeInterface $type */
  $type = $form_state->getFormObject()->getEntity();
  $form['menu']['menu_options'] = array(
    '#type' => 'checkboxes',
    '#title' => t('Available menus'),
    '#default_value' => $type->getThirdPartySetting('menu_ui', 'available_menus', array('main')),
    '#options' => $menu_options,
    '#description' => t('The menus available to place links in for this content type.'),
  );
 $form['#entity_builders'][] = 'menu_ui_form_node_type_form_builder';
}

function menu_ui_form_node_type_form_builder($entity_type, NodeTypeInterface $type, &$form, FormStateInterface $form_state) {
  $type->setThirdPartySetting('menu_ui', 'available_menus', array_values(array_filter($form_state->getValue('menu_options'))));
  $type->setThirdPartySetting('menu_ui', 'parent', $form_state->getValue('menu_parent'));
}

// Then the setting can be used as 
$menu_options = $type->getThirdPartySetting('menu_ui', 'available_menus', array('main'));

Additionally, modules need to provide the config schema for their settings:

node_type.third_party.menu_ui:
  type: mapping
  label: 'Per-content type menu settings'
  mapping:
    available_menus:
      type: sequence
      label: 'Available menus'
      sequence:
       - type: string
         label: 'Menu machine name'
    parent:
      type: string
      label: 'Parent'