I suspect there might be an issue with your fonts. You seem to be installing them at the OS level, which is kinda risky as you need to distribute the ttf file. I believe you would be better off with installing them at LaTeX level, via an appropriate font package. Shinyapps.io runs on Ubuntu, which runs on UTF-8 and should not have issues with Cyrillic (I know it handles Czech well, but haven't tried Cyrillic, and your code doesn't run for me).
You may also consider putting the LaTeX code into a template file, I have found it much easier to troubleshoot than YAML. Have a look at this earlier topic on this matter: