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 (
    2012, 2013, 2014, 2007, 2006, 2000, 2001, 
    1998, 1997, 1993
  ) 
GROUP BY 
  video_id

Query time 0.00037

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "4.26"
    },
    "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": 19,
        "rows_produced_per_join": 19,
        "filtered": "100.00",
        "using_index": true,
        "cost_info": {
          "read_cost": "2.36",
          "eval_cost": "1.90",
          "prefix_cost": "4.26",
          "data_read_per_join": "456"
        },
        "used_columns": [
          "video_id",
          "product_id",
          "type"
        ],
        "attached_condition": "(`cscart_db`.`cscart_cp_video_product_links`.`video_id` in (2012,2013,2014,2007,2006,2000,2001,1998,1997,1993))"
      }
    }
  }
}