So, I managed to determine that NIMA is directly associated with the NGIA and I found a GitHub org for NGIA: https://github.com/ngageoint?page=1
There's an iOS app repo there - https://github.com/ngageoint/anti-piracy-iOS-app which had a CSV file: https://raw.githubusercontent.com/ngageoint/anti-piracy-iOS-app/master/Asam/subregions.csv
That CSV file is a set of "spatial lines" for framing the sub-regions. I had to modify the subregions (I put the modified file in this gist) to remove duplicate IDs.
The R script (below) will convert the CSV tile to a SpatialPolygonsDataFrame and also uses the geojsonio package to make a geojson file of the SPDF (which is also in the repo).
Thank you to everyone who went on the hunt! It's really weird this shapefile wasn't in any catalog (it wasn't in any of the links here).
library(sp)
library(stringr)
dat <- readLines("subregions.csv")
SpatialPolygons(lapply(dat, function(x) {
region <- str_split_fixed(x, ",", 2)[,1]
poly_pts <- as.numeric(str_split(str_split_fixed(x, ",", 2)[,2], ",")[[1]])
poly_mat <- matrix(c(poly_pts, poly_pts[1], poly_pts[2]), ncol=2, byrow=TRUE)
tmp <- poly_mat[,2]
poly_mat[,2] <- poly_mat[,1]
poly_mat[,1] <- tmp
Polygons(list(Polygon(poly_mat)), ID=region)
}), proj4string=CRS("+proj=longlat")) -> subr
subr_dat <- data.frame(id=sapply(subr@polygons, function(x) { slot(x, "ID") }),
stringsAsFactors=FALSE)
rownames(subr_dat) <- subr_dat$id
subr <- SpatialPolygonsDataFrame(subr, subr_dat)
plot(subr)
library(geojsonio)
geojson_write(subr, geometry="polygon", file="subregions.geojson")
results in this gist