Any easy test of “more old white men dying” for the New Zealand Data is the Statistics New Zealand (Infoshare) Death Rates, Age-specific death rates by sex, December years (total population) as it gives the death rate for each age band across years (though it doesn’t seperate out ethnicity, European ancestors is the majority of people in question). The csv file used is a download of male and female deaths for all age bands for all years. Though Case and Deaton used 45-54, to match that exactly I would need to download the raw death numbers and the total population and do a bit of maths, but I can do this quick check from the one source easily (so one chart for 45-49, one chart for 50-54). Males are purple (#af8dc3), females are green (#7fbf7b). Original data is per thousand, I have scaled it to per 100000 to match Case and Deaton

nz <- read.csv("DMM168901_20151107_023104_35.csv", skip=2, nrows = 44)
names(nz)[1] <- "year"
plot(nz$year, nz$X45.49.Years * 100, ylim=c(0,1000), xlab="year", ylab="Death Rate", main="Middle aged (45-49)\nNew Zealanders are dying less\nover time", type="l", col="#af8dc3", frame.plot=F)
lines(nz$year, nz$X45.49.Years.1 * 100, col="#7fbf7b", lty=6)
text(2010,300,"Male", cex=0.6, col="#af8dc3")
text(2010,100,"Female", cex=0.6, col="#7fbf7b")

plot(nz$year, nz$X50.54.Years * 100, ylim=c(0,1000), xlab="year", ylab="Death Rate", main="Slightly older Middle aged (50-54)\nNew Zealanders are dying less\n especially males", type="l", col="#af8dc3", frame.plot=F)
lines(nz$year, nz$X50.54.Years.1 * 100, col="#7fbf7b", lty=6)
text(2010,400,"Male", cex=0.6, col="#af8dc3")
text(2010,200,"Female", cex=0.6, col="#7fbf7b")