The difference between what you're looking at is about App Engine Standard vs App Engine Flexible (formerly known as Managed VMs). NodeJS is only supported on App Engine Flexible.
App Engine Standard has some advantages (faster deployer times, ability to "scale to zero" so you pay nothing for idle apps), but it's much less flexible in that many libraries are not available in the runtimes and so you rely more heavily on App Engine APIs. To provide a way to test it locally, the local development server was provided.
Standard supports Python, Java, Go, and PHP. However, even with those languages, you still might choose Flexible if you want to do something like use Java 8, Python 3, or custom libraries like imagemagick.
App Engine Flexible is a pretty different product, although on the surface it looks similar since it has similar tooling and configuration, and they are both scalable platform-as-a-service products. But the concept is that you bring whatever environment you're familiar with it, and it runs it in a container (which is hidden from you. unless you use Custom runtimes to builds your own Docker runtime for it).
Since you're bringing your standard development environment to App Engine, the idea is you test your Node app the same way you would test any other Node app, and run it like you would run other local Node projects locally. There's not supposed to be too much special about the App Engine flexible environment, by design, so there's no need for a special local testing server.
However, if you're using Cloud Datastore, emulators are provided so you can run tests more quickly and without paying any money. So the emulator is definitely what you're looking for to do local unit tests. If you have any problems or issues with it, you should followup with more questions on Stack Overflow.
If you haven't seen already, there is a Getting Started with Node app that uses App Engine Flexible, and demonstrates a variety of tasks using Cloud Datastore, as well as MongoDB and CloudSQL (managed MySQL).
https://github.com/googlecloudplatform/nodejs-getting-started
