SELECT 
  pair_id, 
  v.video_id, 
  video_url_id, 
  source, 
  position 
FROM 
  cscart_videos as v 
  INNER JOIN cscart_videos_links as vl ON v.video_id = vl.video_id 
WHERE 
  object_id = 313159 
  AND vl.object_type = 'product' 
ORDER BY 
  position

Query time 0.00361

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost": 0.0051722,
    "nested_loop": [
      {
        "read_sorted_file": {
          "filesort": {
            "sort_key": "vl.position",
            "table": {
              "table_name": "vl",
              "access_type": "ref",
              "possible_keys": ["object_id", "video_id"],
              "key": "object_id",
              "key_length": "53",
              "used_key_parts": ["object_id", "object_type"],
              "ref": ["const", "const"],
              "loops": 1,
              "rows": 1,
              "cost": 0.00345856,
              "filtered": 100,
              "index_condition": "vl.object_type = 'product'",
              "attached_condition": "vl.object_id <=> 313159 and vl.object_type <=> 'product'"
            }
          }
        }
      },
      {
        "table": {
          "table_name": "v",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY"],
          "key": "PRIMARY",
          "key_length": "4",
          "used_key_parts": ["video_id"],
          "ref": ["u985510652_ecartify.vl.video_id"],
          "loops": 1,
          "rows": 1,
          "cost": 0.00171364,
          "filtered": 100
        }
      }
    ]
  }
}