I totally agree downloading the menu as a pdf file is a bad solution, a terrible user experience, especially on mobile.

In a somewhat similar situation, when I was in Croatia last month I was surprised to see that one restaurant instead of having a stand with the menu to browse (like most other establishments) had QR codes on every table instead of traditional written menus. It took me a while to get the message that the list of dishes was hidden behind the code (there was no text provided, just an empty table with a QR code). We chose a different place.

As for the theme, it looks decent. I followed the link and had a closer look.