Is the attorney docket number used primarily for the attorney to keep track of the application in their own docket management software?

Yes, a docket number is an identifier for attorney client matters (and it is not merely limited to patent applications).  There is usually a client identifier followed by a matter identifier, because the same client could have engaged the law firm for multiple matters.  At one of my earlier firms, the attorney docket number had this format:

[Client Name].[Matter Number]

For example:

Apple.003PRV

In this case, the Client was "Apple, Inc."  and this was the third matter that the law firm handled for them, which happened to be a provisional patent application.

Many of the larger firms prefer using numbers, instead of names, to identify their clients.  There is a good reason for this--the client could change their business name sometime in the future.  Suppose Apple, Inc. changed its business name to Orange, Inc.  If they did that, the law firm would have to update the docket numbers on all of their past filings, which could be hundreds of filings.   But if they instead used a numeric identifier  to identify their client, they could just change one entry in their internal client list.   So Instead of 10324 = Apple, Inc., they could just change that to 10324 = Orange, Inc., and all cases could stay docketed as 10324.00x.