To me the main readability problem of the first example is that it does the head...

ummonk · on Jan 25, 2019

The 2nd one would be significantly more readable with explicit typing (to make it clear that you're dealing with a pointer to pointer).

Though I think putting the head check at the beginning like you said will make the first example very reasonable (and relatively compact too).

  remove_list_entry(entry)
  {
      if (head == entry) {
          head = entry->next;
      } else {
          prev = head;
          while (prev->next != entry) {
              prev = prev->next;
          }
          prev->next = entry->next;
      }
  }