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 (
    2272, 2273, 2275, 2277, 2225, 2207, 2215, 
    2216, 2217, 2220
  ) 
GROUP BY 
  video_id

Query time 0.00042

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "5.67"
    },
    "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": 26,
        "rows_produced_per_join": 26,
        "filtered": "100.00",
        "using_index": true,
        "cost_info": {
          "read_cost": "3.07",
          "eval_cost": "2.60",
          "prefix_cost": "5.67",
          "data_read_per_join": "624"
        },
        "used_columns": [
          "video_id",
          "product_id",
          "type"
        ],
        "attached_condition": "(`cscart_db`.`cscart_cp_video_product_links`.`video_id` in (2272,2273,2275,2277,2225,2207,2215,2216,2217,2220))"
      }
    }
  }
}

Result

video_id products
2207 0, 37830, 39919, 39924, 65550, 66727, 67925
2216 36710, 65546
2217 39921, 39922, 39924
2220 39916
2225 33114, 37916, 68614, 68899, 68901, 68903, 68921, 69310
2272 31377
2273 31336
2275 38512
2277 66500