The problem with server is actually not a server's problem. I opened Kitematic and saw a console with an error message saying that there is no such directory (DOCUMENT ROOT) to show its contents.
Then I was playing with configs and finally realized what they are for. I found that docker-compose.yml tells which directories to put inside a certain container, so the "app" service asks for following directories:
- ./application:/project
- ./cache:/project/cache
- ./logs:/project/logs
- ./conf/php/cli.ini:/etc/php/7.0/cli/conf.d/100-custom.ini
- ./conf/php/fpm.ini:/etc/php/7.0/fpm/conf.d/100-custom.ini
It is intended to put "application" inside container's "/project" and so on. The only problem is that these folders are empty. It only creates project/cache and project/logs but there is no "public" directory which should've been compied to "/project" from "application".