SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    687, 672, 673, 674, 688, 675, 689, 676, 
    690, 697, 677, 698, 678, 691, 679, 680, 
    681, 682, 683, 684, 692, 693, 694, 670, 
    671, 685, 696, 686, 700, 695, 699, 701
  ) 
  AND category_id != 265

Query time 0.00090

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_categories",
      "access_type": "range",
      "possible_keys": ["PRIMARY", "parent", "p_category_id"],
      "key": "parent",
      "key_length": "3",
      "used_key_parts": ["parent_id"],
      "rows": 55,
      "filtered": 100,
      "index_condition": "cscart_categories.parent_id in (687,672,673,674,688,675,689,676,690,697,677,698,678,691,679,680,681,682,683,684,692,693,694,670,671,685,696,686,700,695,699,701)",
      "attached_condition": "cscart_categories.category_id <> 265"
    }
  }
}

Result

category_id parent_id
671 670
686 670
672 671
673 671
674 671
675 671
676 671
677 671
678 671
679 671
680 671
681 671
682 671
683 671
684 671
685 671
687 686
688 686
689 686
690 686
691 686
692 686
693 686
694 686
695 686
697 696
698 696
699 696