dockerd needs to be started with root. To see how to run dockerd in rootless mode with unprivileged user, see the documentation code example

Example 1: make docker sudo less

$ sudo groupadd docker
$ sudo usermod -aG docker $USER
$ newgrp docker

Example 2: setting docker as a non root user

##########################################
# Dockerfile to change from root to 
# non-root privilege
###########################################
# Base image is CentOS 7
FROM Centos:7
# Add a new user "john" with user id 8877
RUN useradd -u 8877 john
# Change to non-root privilege
USER john