you can also Count Email click

I've noticed you can also count click on email field.

I would start with a

if ($form_id == "field_ui_field_edit_form" && ($form["#field"]["type"] == "link_field" || $form["#field"]["type"] == "email"  ) ) {

in your function link_click_count_form_alter(&$form, &$form_state, $form_id)

Hope will help