No DAC connection could be established on the default port. Make sure DAC is enabled
From Using a Dedicated Administrator Connection:


  By default, the connection is only allowed from a client running on the server. Network connections are not permitted unless they are configured by using the sp_configure stored procedure with the remote admin connections option.


From that latter page:


  SQL Server provides a dedicated administrator connection (DAC). The DAC lets an administrator access a running server to execute diagnostic functions or Transact-SQL statements, or to troubleshoot problems on the server, even when the server is locked or running in an abnormal state and not responding to a SQL Server Database Engine connection. By default, the DAC is only available from a client on the server. To enable client applications on remote computers to use the DAC, use the remote admin connections option of sp_configure.


I think the page you read is just a little light on the details, that's all.

As for why a local DAC connection might not work, it's possible that it's because you're running SQL Server Express, which requires TF 7806 to enable. Another possibility is the network protocols that are enabled.