I don't think it's an easy one: X11 is what some operating systems (Linux typically) use to display windows.
So in your case, I don't think the error comes from
shiny::runApp, I suspect it comes from a function inside the app that is trying to open a window. Does your error message have more lines that you didn't copy? Something like:
Warning: Error in : Please install X11 library to use this function.
My guess is that you're attempting to run the app on a computer that doesn't support X11 (for example a server with no GUI), and the app is trying to open a plot window. This should be unnecessary for a Shiny app: the plots should be displayed in the browser, not in a separate window.
If I'm right, the only way to solve it is to look at the code of the app and figure out where that call is, and why it was needed.
One last weird thing: this error message doesn't look like atypical R error message. Did you translate it from another language? If not, that suggests to me that the author of the app wrote it, and may be referring to some internal library.