httpuv's static file serving doesn't currently support range requests (i.e. requests for only part of a file). This would be very useful! servr supports this, but by reading the static content into memory first rather than reading from disk (see yihui/servr#35 and yihui/servr#41).
The need for range request support in httpuv/shiny has been mentioned in various places, see e.g.:

• byte serving capability in shiny:::staticHandler shiny#747 (but that PR not merged, and I don't think it will work now anyway because static file handling is now deferred by default to httpuv, not handled by shiny itself)
• https://community.rstudio.com/t/range-requests-in-pdf-js-used-in-r-shiny/11488
• https://stackoverflow.com/questions/49624699/adding-http-headers-in-shiny-to-play-audio
• emuR uses something very similar to servr's implementation: https://github.com/IPS-LMU/emuR/blob/master/R/emuR-server.R#L247

Range request support in shiny should (?) be relatively straightforward once httpuv supports it, just requiring a couple of extra headers to be passed to the shiny app.