The ways to connect to your instances in the Cloud are limited. For Linux, it would be through either the Google Cloud Platform Console or the gcloud command-line tool. You can connect to a Windows instance using graphical connection tools, such as Chrome RDP. You can find more detail on the "Connecting to Instances" documentation page.
In case of Windows, it is possible use these graphical capabilities to edit your code directly on your VM image; this should spare you the effort of using VIM commands. You may even consider installing IntelliJ on your Windows instance.
In any case, taking into consideration the limited nature of remote connection, you won't be able to edit your code on your local machine using IntelliJ, and running it via remote connection on a GCE instance by means of IntelliJ commands.