The REST API service is exposed on port 8008 on the rest-api container, and also forwarded to port 8008 on the host:
rest-api:
  image: sawtooth-rest-api:latest
  container_name: sawtooth-rest-api-default
  expose:
    - 8008
  ports:
    - "8008:8008"
  depends_on:
    - validator
  entrypoint: sawtooth-rest-api --connect tcp://validator:4004 --bind rest-api:8008
The service should therefore be accessible from another Docker container as http://rest-api:8008/blocks or from the host as http://127.0.0.1:8008/blocks via a web browser or curl. If it does not work, try changing the entrypoint command to use --bind 0.0.0.0:8008 as the last argument.