That’s called Home Assistant Container.
Home Assistant Core is, as callifo described, simply python code. So if the discussion involves docker, it can’t be about Home Assistant Core but about Home Assistant Container or even Home Assistant Supervised or Home Assistant OS. Of the four, only Home Assistant Core doesn’t involve the use of docker.
If you want to use Home Assistant Core then it isn’t distributed as a docker container (just python code).
Given the docker-compose file you posted, what you want is Home Assistant Container.