I'm a little confused here. What is the intention of the article? To avoid unnecessary Sort operators in the execution plan or to eliminate ORDER BY and still get the results sorted?

If the idea is to eliminate the need for ORDER BY then what this article describes should not be trusted. There is no guarantee that an index (clustered or non-clustered) will return the result in an ordered manner. IT might work today, but what happens when the amount of data or statistics changes? Will the QO find a better plan and havoc the ordered results that used to be returned to the client? It might very well do so.

There is only one way to guarantee ordered results. Say it after me: ORDER BY.

On the other hand, if you don't want SQL Server to waste memory, disk I/O and CPU on sorting, then you could send the result to the client and let it do the sorting. There is usually lots of unused CPU capacity on the client computers.