Can QGIS open the file type .pitemx or .pkinfo?

Yes and no. It takes a bit of doing/navigating, but under 3.18 at least, you can access the ArcGIS Server REST endpoint to add the data to your local project with ease.

In other cases, you could accomplish it by loading the *.lyr files using SLYR by North Road/Nyall Dawson.

Getting the REST endpoint URL is possible by opening your linked item in the web viewer:

then selecting the triple dots on it in the Web Map Content to Show Item Details, and then clicking Source: Map Service under Details to get to the ArcGIS REST endpoint.

From there, copy the URL for the services breadcrumb (in this case, https://services.arcgisonline.co.nz/arcgis/rest/services)
and create a new connection under the Data Source Manager for ArcGIS REST Server.

You should see the data listed out like this: