SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    1201, 1720, 1114, 1121, 1742, 1113, 1115, 
    1122, 1641, 1177, 1640, 1095, 1634, 
    1741, 1639
  ) 
  AND category_id != 1

Query time 0.00028

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": 16,
      "filtered": 100,
      "index_condition": "cscart_categories.parent_id in (1201,1720,1114,1121,1742,1113,1115,1122,1641,1177,1640,1095,1634,1741,1639)",
      "attached_condition": "cscart_categories.category_id <> 1"
    }
  }
}