The author of the blog post chose an area that doesn't render well. The various issues are being flagged in the relevant repositories as they are found.
Recent versions of QGIS support vector tiles in the MVT format (like these ones). So with a suitable style you should be able to create a layout using vector tiles and print.
Assuming you meet the relevant attribution/license requirements for the various bits you choose of course. I don't think any usage policy has been published for these tiles yet.
Unfortunately there are some translation issues with styles for MVT sources so you might need to do a bit of fixing if you don't want to go the route of a paid plan with MapTiler (third party provider) who have a plugin.
The tile schema being used for the current testing (shortbread) doesn't support many languages, but they I think those working on this want to support them once the bugs are worked out.
For an example of how this might look see e.g. https://americanamap.org which uses OSM data, but doesn't aim to be near live like the tiles this thread is about.
It's called vandalism on OpenStreetMap too. New users often make mistakes though and some Pokemon Go users might become more productive when they realise the map is used for other things too so a bit of guidance can be useful as the changes get reverted.
IIRC many of the original employees were ex-Googlers and the original Ingress game did use Google Maps data so at some level they were able to get what they need. I think there were rumours about them using undocumented abilities too in the early days, but my memory is fuzzy at this point. They moved to OSM later.
The author of the blog post chose an area that doesn't render well. The various issues are being flagged in the relevant repositories as they are found.