I would consider a project in Docker serverless if it is used in something like AWS EC2 Container Service (ECS).
Why? Even with ECS the container's host is maintained by you . It's hardly more "serverless" (less serverful?) than just running docker on EC2.
If configured properly everything in an ECS stack is a service offered by AWS:
AMI maintenance is a service provided by the ECS team
The ASG service automates cluster side
CloudWatch Logs service ingests all your logs and offers archival and search services
ELB and ALB are managed services
CloudFormation service can configure all this.
I live in a world where I configure all this but maintenance is trending way down.
It's not zero like on Heroku but maybe it's a happy trade off for the extra customization...