To resolve this issue:

  1. Open the project in any of QuarkXPress 7.x versions and Export it down to version 6.0.

  2. Open the down-saved project in QuarkXPress 6.5

  3. Go to File > Export layout as PDF. In the PDF Options dialog, in the Job Options tab, select Embed All fonts.

  4. Save the PDF

  5. Save the project in QuarkXPress 6.5

  6. Open the project in QuarkXPress 7 and export a PDF with the default setting.

Fonts will be embedded correctly in the PDF.