I would check out using an knitr::include_app(url). This wraps around an iframe which allows displaying external urls (or shiny applications). Videos can be displayed directly on the site, but shiny applications need a backend server to process what is happening.
For more a live example, check out: https://bookdown.org/yihui/bookdown/web-pages-and-shiny-apps.html
```{r}
knitr::include_app("https://gallery.shinyapps.io/001-hello/", height = "500px")
```
You can also do this manually by adding an iframe directly. Change the src in the line below to point to an already hosted shiny application.
<iframe src="https://gallery.shinyapps.io/001-hello/" width="100%" height="500px" style="border:none;">