I am also attempting to install it on Server 2016. I followed their instructions, which are rather simple, but I am also unable to install it. My error is a bit different though:
PS I:\DOCKER> .\bitwarden.ps1 -install
_ _ _ _
| |__ (_) |___ ____ _ _ __ __| | ___ _ __
| '_ \| | __\ \ /\ / / _` | '__/ _` |/ _ \ '_ \
| |_) | | |_ \ V V / (_| | | | (_| | __/ | | |
|_.__/|_|\__| \_/\_/ \__,_|_| \__,_|\___|_| |_|
Open source password management solutions
Copyright 2015-2019, 8bit Solutions LLC
https://bitwarden.com, https://github.com/bitwarden
===================================================
Docker version 18.09.2, build 1ac774dfdd
docker-compose version 1.23.2, build 1110ad01
(!) Enter the domain name for your Bitwarden instance (ex. bitwarden.company.com):
(!) Do you want to use Let's Encrypt to generate a free SSL certificate? (y/n): y
error during connect: Post http://%2F%2F.%2Fpipe%2Fdocker_engine/v1.39/images/create?fromImage=bitwarden%2Fsetup&tag=1.29.0: open //./pipe/docker_engine: The system cannot find the file specified. In the default daemon configuration on Windows, the docker client must be run elevated to connect. This error may also indicate that the docker daemon is not running.
C:\Program Files\docker\docker.exe: error during connect: Post http://%2F%2F.%2Fpipe%2Fdocker_engine/v1.39/containers/create?name=setup: open //./pipe/docker_engine: The system cannot find the file specified. In the default daemon configuration on Windows, the docker client must be run elevated to connect. This error may also indicate that the docker daemon is not running.
See 'C:\Program Files\docker\docker.exe run --help'.
PS I:\DOCKER> Get-Service docker
Status Name DisplayName
------ ---- -----------
Running docker Docker Engine
PS I:\DOCKER>
any thoughts or help would be appreciated.