What is meant by "Stand-Alone Instance of SQL Server"
Stand Alone:


  Operating, functioning, or existing without additions or assistance; independent; able to be separate or separated.


And that's precisely what is referring to on that article, to a self-sustained SQL Server instance, not participating (as Aaron commented) on a Failover Cluster or a WSFC. That's why the article refers to some scenarios where renaming there computer is directly forbidden or it could wreak havoc as it's not a "stand alone" but part or some other process.