Somehow, I struggled through Docker. I will outline my steps so that you don't have to follow the tedious path.
First I tried to install Docker on Windows.
Pitfalls: OS version. If you don't have the Windows 10 Pro edition, you can use the Docker toolbox only.
So, okay. Download the Docker toolbox.
And I checked the VirtualBox option for good measure and it did stand me in good stead because - believe this - the Windows Server image on the EC2 instance cannot have its Hyper-V/AMD something started because you can set the setting only in BIOS and on the EC2 instance, running on Remote Desktop (RDP), there is no way of accessing the BIOS, even if it made sense!
2nd attempt
I went into the VM using the RDP and started the VirtualBox and gave Ubuntu as the image. Great! It started the VirtualBox but the EC2 instance had only 1 GB RAM and the VirtualBox script wanted 2 GB, by default!
Okay! Let me check if an EC2 instance with a Linux Ubuntu image (AMI) was available. It was but I did not want to get into the Linux OS shell.
So, what is the alternative?
Docker EE for AWS
A native AWS stack that could host a Docker container on a kernel all its own, with a set of Docker engines. No underlying OS but on top of the AWS IaaS services!
Sounds great but you really cannot see it working because when you try to access the public DNS via a browser, an Apache server message will greet you that the url you are looking for cannot be reached although the server is okay!
Docker EE for AWS is a one click template to quickly deploy Docker on Amazon EC2, says the Docker EE Store. And it is, if only the template stayed put in its AWS region. It seems that the tricky part has not been documented.
The KeyPair that the template requires must be an EC2 generated Keypair from the same region in which your EC2 instance is!
Finally, the aws CloudFormation Stack gets created.