I figured it out!
Instead of docker run heroiclabs/nakama I just cleared out all containers, and then pulled it the nakama container, and ran docker-compose -f docker-compose-postgres.yml.
From there, connecting from DBeaver requires the Droplet IP address, port: 5432, database: nakama, username: postgres, and password: localdb (as defined in the yml).
Leaving this here as this took a while to figure out, so partially to remind myself, and also for anybody else interested.