SELECT 
  video_id, 
  GROUP_CONCAT(
    DISTINCT product_id 
    ORDER BY 
      product_id ASC SEPARATOR ', '
  ) as products 
FROM 
  cscart_cp_video_product_links 
WHERE 
  video_id IN (
    1945, 1934, 1926, 1925, 1924, 1923, 1920, 
    1919, 1916, 1914
  ) 
GROUP BY 
  video_id

Query time 0.00038

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "3.45"
    },
    "grouping_operation": {
      "using_filesort": false,
      "table": {
        "table_name": "cscart_cp_video_product_links",
        "access_type": "range",
        "possible_keys": [
          "PRIMARY",
          "position",
          "video_id_idx",
          "idx_product_type_position"
        ],
        "key": "video_id_idx",
        "used_key_parts": [
          "video_id"
        ],
        "key_length": "3",
        "rows_examined_per_scan": 14,
        "rows_produced_per_join": 14,
        "filtered": "100.00",
        "using_index": true,
        "cost_info": {
          "read_cost": "2.05",
          "eval_cost": "1.40",
          "prefix_cost": "3.45",
          "data_read_per_join": "336"
        },
        "used_columns": [
          "video_id",
          "product_id",
          "type"
        ],
        "attached_condition": "(`cscart_db`.`cscart_cp_video_product_links`.`video_id` in (1945,1934,1926,1925,1924,1923,1920,1919,1916,1914))"
      }
    }
  }
}