How to install Barman with pg_receivewal and pg_basebackup without install PostgreSQL server?
Actually the given URL also says in the System requirements section: 


Linux/Unix
Python &gt;= 3.4
Python modules:
    argcomplete
    argh &gt;= 0.21.2
    psycopg2 &gt;= 2.4.2
    python-dateutil
    setuptools
PostgreSQL &gt;= 8.3
rsync &gt;= 3.0.4 (optional for PostgreSQL &gt;= 9.2)



It looks like you need to install PostgreSQL server.