Word 2013 export to PDF how to keep font vectorized

This is indeed a problem. and it still exists in Office 2016. There is a documented feature (aka bug) that Office doesn't know (or want) how to embed Open Type fonts, unless they have a True Type equivalent.

Starting with Windows 10, there is a new printer installed in the system called "Microsoft Print to PDF":

If you use that, instead of using the export to PDF feature, it actually works just fine. It properly embeds the fonts in vector format and is readable on devices that do not have the font installed.