I am afraid it's not that easy.
The piarchive file itself has no information about a points name because internally the point ID is used. The point table maps point ID's with point names. So what could work here is restoring a PI Backup or restoring a PI Backup partly. This however depends on how many PI Points are licensed. Assuming your PI System would be a Personal Development PI System as it is included with the paid PI Developers Club membership (please see our FAQ's for details), you would be limited to 10,000 PI Points and the license would allow you to restore a PI Backup from another PI Data Archive installation with up to 10k PI Points.
Piconfig.exe is a command line tool that is intended for administrative tasks and pretty handy on importing and exporting data for single PI Points. To give you an idea what this approach is about, please have a look at KB00848 - Backfilling with PIconfig
Another approach could be a custom application that retrieves archived data and stores it in flat files e.g. a comma separated file for each PI Point and a second custom application that reads the flat files and inserts the data to the destination. I would suggest using AF SDK for such a programming solution. This solution can as well be combined with the previous one e.g. if the application retrieving the data from the source would create piconfig input scripts.
Please note that with earlier PI Data Archive versions (before PI 2012), it was necessary to prepare archive files of the destination. The before mentioned knowledge base article has a related section titled Prepare the PI Server for backfilling
Assuming the source PI System is larger than the destination, the leading question would be how many PI Points you like to replicate.
You will need a PI System Backup from your "client" to be able to restore it on your system.
There is a procedure available here:
More information on backups: