The key used is actually Public API when code is using Private API endpoint. When creating the key, the option "Select Private API key" may not exist. In that case, it is needed to reach out to Dailymotion Account Manager or Dailymotion Support Team so they could enable it.

Private API would not be available for all Partners https://faq.dailymotion.com/hc/en-us/articles/5483274630930-Create-and-manage-your-API-keys

If you would like to have it, you may become Dailymotion Pro subscriber https://pro.dailymotion.com/en/