Stackdriver enlists many other resources but it is not listing the clusters that were created before enabling Stackdriver. From the doc, I am able to view the cluster newly created. However, for the existing clusters, the Kubernetes BETA section is not showing them despite I have upgraded the cluster version.
Also, I could not tick mark the "Try the new BETA version" while editing the cluster.
As the article and also this public document mentioned, this release of Stackdriver Kubernetes Monitoring is supported only on new Kubernetes Engine clusters using Kubernetes v1.10 or later version. That means you can't migrate existing clusters to the new monitoring option. Currently, this is indeed not clearly mentioned on this documentation which you are following. I can certainly advise our documentation team to reflect this. That being said, it is expected behavior as such migrate existing clusters to the new monitoring option is not possible at this moment.