3rd party theme update mechanism

As per new requirements, themes may include an update mechanism.
Unfortunately, I wasn’t able to find out whether theme authors are allowed to use a 3rd party website such as wp-updates.com to create this mechanism or not?

Any confirmation by the review team is also appreciated.

You’re not allowed to do it. You can suggest the users to install Envato plugin that handles the updates automatically.

Have you read the requirements? It says and I quote:

themes may include an update mechanism.

The question is how?

Use Envato plugin