Here is a base R approach that will get you all 227 areas with data.
First, get all the areas available with DataStructureMethod. Then split the list into sets of 25 areas so that the API won't fail. Create a new empty list to hold the returned data. Next, use a for loop to iterate over all the area sets and store the results into a list element.
library(IMFData)
databaseID <- "DOT"
startdate = "2013-01-01"
enddate = "2019-12-31"
areas <- DataStructureMethod("DOT")$CL_COUNTERPART_AREA_DOT$CodeValue
areas.list <- split(areas, ceiling(seq_along(areas)/25))
result.list <- list()
for(i in seq_along(areas.list)) {
  filter <- list(CL_FREQ = "M", CL_AREA_DOT = areas.list[[i]], CL_INDICATOR_DOT = "TXG_FOB_USD", CL_COUNTERPART_AREA_DOT = "W00")
  result.list[[i]] <- CompactDataMethod(databaseID, filter, startdate, enddate)
}
Now that we have all the data, we can extract the @OBS_VALUE from each area. So we can keep up with which is which, we will assign the column names to @REF_AREA. Then all we need to do is cbind all the areas together and add a time period column.  
result <- sapply(result.list,function(x){y <- sapply(x$Obs,function(y){y[['@OBS_VALUE']]}); colnames(y) <- x[["@REF_AREA"]]; y})
result <- do.call(cbind,result)
result <- cbind(timeperiod = result.list[[1]]$Obs[[1]][['@TIME_PERIOD']],result)
result[1:10,1:10]
      timeperiod BB          BM         AF          BS           AL           AW          BD            BZ          AO           
 [1,] "2013-01"  "28.609779" "2.763473" "37.545734" "140.793072" "182.268383" "15.248257" "2135.314764" "26.993657" "5738.361548"
 [2,] "2013-02"  "31.408923" "2.588724" "23.319418" "51.207085"  "160.256056" "13.357883" "1883.921679" "31.959256" "5093.785673"
 [3,] "2013-03"  "26.490062" "2.161194" "34.313418" "116.533489" "187.347118" "11.807801" "2074.639533" "36.975964" "5836.777823"
 [4,] "2013-04"  "30.969022" "6.541486" "27.46926"  "79.9772"    "199.063249" "15.363928" "1996.029477" "39.84747"  "4953.276187"
 [5,] "2013-05"  "27.633188" "3.030127" "32.675746" "765.5369"   "221.793898" "13.232063" "2247.850876" "73.201747" "5425.804703"
 [6,] "2013-06"  "24.064953" "2.816781" "29.454347" "60.756462"  "201.765833" "13.698186" "2291.680871" "32.821853" "5271.431577"
 [7,] "2013-07"  "26.25563"  "2.657042" "15.540238" "95.12846"   "233.746903" "14.499091" "2359.924118" "33.763333" "5666.628083"
 [8,] "2013-08"  "26.85187"  "2.883294" "21.369248" "74.317362"  "180.045606" "15.545374" "1985.100494" "31.342921" "5557.632778"
 [9,] "2013-09"  "25.025515" "3.368449" "26.061924" "89.380055"  "211.352443" "12.323627" "2441.630301" "25.107398" "5558.266666"
[10,] "2013-10"  "34.040048" "3.249082" "49.352241" "128.44329"  "227.724296" "17.172523" "2131.788729" "28.489788" "5411.943251"
As you probably know, the names of those areas are available in DataStructureMethod("DOT")$CL_COUNTERPART_AREA_DOT.