It is certainly not possible in Google App Engine Standard environment but I have been told it is likely to be possible in Flexible environment.
Is this correct and if so how to do this?
If not, then what Google Cloud Platform solution except Compute Engine would fit my requirement to run an .exe?
App Engine Flexible uses VMs with Linux images as the host machine, which then run Docker containers, so I don't believe this is currently possible. Microsoft has been talking about Windows containers, but I believe they can only run on Windows hosts which App Engine Flexible does not currently support.
https://msdn.microsoft.com/en-us/virtualization/windowscontainers/quick_start/quick_start_windows_server
The only way I can think of to run a Windows exe on App Engine flexible would be to figure out a way to run the Windows exe on Linux, which may be possible with something like WINE. Take a look at this question here:
https://superuser.com/questions/216629/can-i-run-a-windows-exe-file-on-linux
If I had to guess, this is likely what the person who told you this was possible had in mind.
In the Container Engine world, supporting Windows containers is a topic of discussion in Kubernetes, which may eventually end up in Container Engine, but as you can see all these ideas are still early development stages:
https://github.com/kubernetes/kubernetes/issues/22623
