Crude way (I'll update this in a sec): 
ini::read.ini("https://rud.is/dl/example.url")$InternetShortcut$URL
## [1] "https://rud.is/b/2017/11/11/measuring-monitoring-internet-speed-with-r/"
Made slightly less crude:
read_url_shortcut <- function(x) {
  require(ini)
  x <- ini::read.ini(x)  
  x[["InternetShortcut"]][["URL"]]
}
Without the ini package dependency:
read_url_shortcut <- function(x) {
  x <- readLines(x)
  x <- grep("^URL", x, value=TRUE)
  gsub("^URL[[:space:]]*=[[:space:]]*", "", x)
}
More "production-worthy" version:
#' Read in internet shortcuts (.url or .webloc) and extract URL target
#' 
#' @param shortcuts character vector of file path+names or web addresses
#'        to .url or .webloc files to have URL fields extracted from.
#' @return character vector of URLs
read_shortcut <- function(shortcuts) {
  require(ini)
  require(xml2)
  require(purrr)
  purrr::map_chr(shortcuts, ~{
    if (!grepl("^http[s]://", .x)) {
      .x <- path.expand(.x)
      if (!file.exists(.x)) return(NA_character_)
    }
    if (grepl("\\.url$", .x)) {
      .ini <- suppressWarnings(ini::read.ini(.x)) # get encoding issues otherwise
      .ini[["InternetShortcut"]][["URL"]][1] # some evidence multiple are supported but not sure so being safe
    } else if (grepl("\\.webloc$", .x)) {
      .x <- xml2::read_xml(.x)
      xml2::xml_text(xml2::xml_find_first(.x, ".//dict/key[contains(., 'URL')]/../string"))[1] # some evidence multiple are supported but not sure so being safe
    } else {
      NA_character_
    }  
  })
}
Ideally, such a function would return a single data frame row with all relevant info that could be found (title, URL and icon URL, creation/mod dates, etc). I'd rather not keep my Windows VM up long enough to generate sufficient samples to do that.
NOTE: Said "production"-ready version still doesn't gracefully handle edge cases where the file or web address is not readable/reachable nor does it deal with malformed .url or .webloc files.