His site does not seem to provide a space for readers to comment, so I would like to do it here.
First of all, a good way to describe this map would be not simply as a map of world's railroads, but rather as a map of (almost) all railroads, of any type, that ever existed prior to ca. 1990.
There are two reasons for this situation.
(1) First, a map like this brings to the fore a major issue for creating any railway map: the adequacy of sources. It seems that sometimes it is not easy for a newly-built railway to get to maps (especially published in other countries); but it is even harder for a dismantled railway to disappear from maps! The most prominent example visible of Rankin's map is perhaps the Newfoundland Railway, closed for good in 1990, but still gracing many world maps with its presence. Less visible is the Kettle Valley Railway southern British Columbia. Its western section, abandoned in the early 1960s, is gone from most maps (including Rankin's), but the eastern section, physically dismantled in the early 1990s, keeps living in the world of maps, including this one.
As a more interesting example, a good section of Stalin's pet project, the Salekhard–Igarka Railway in the north of western Siberia - namely, an east-west section across the northern part of Tyumen Region - actually saw trial service for a short time before the incomplete rail line was abandoned in 1953, and some western maps at the time showed the western half of this Arctic railway as operational. (I own a 1950s-vintage Rand McNally atlas which does so). Although that railway did not take root in the world of cartography, it somehow made its way into Rankin's masterpiece - presumably because the author tried to work with the most comprehensive sources available.
On the other hand, some of the more recently built railways - e.g., the China-Kazakhstan connection and the Turkmenistan-Iran connection, both activated in the early 1990s - aren't on the map, nor is the Kashgar railway in China's Xinjiang (also built in the 1990s; and it now has branches that only became operational after 2008...)
A peat railway, near Esterwegen, Germany
(2) Second, more detailed maps try to distinguish different types of railways, but in this comprehensive map it apparently was not possible. But a distinction we must make. For example, anyone used to looking at general-purpose maps of Russia and China can't but be amazed at some small but extra-dense clusters of rail lines which, according to Rankin's map, exist in the north-east of European Russia (roughly, the region between Arkhangelsk, Nizhny Novgorod (Gorkiy), and Yekaterinburg (Sverdlovsk), and in China's Heilongjiang and Jilin provinces (the northeastern part of what we used to call Manchuria). There is no mystery here, however: these are so-called logging railways (and, on rare occasions, peat railways). They are very different from standard, permanent, railways operating in these countries. A logging railway is typically a narrow-gauge railway, laid at the minimal cost, and only used to move logs from the woodlots to a mainline railway station or a sawmill. I understand that many sections of such railways are only used for a few years, and then, once that particular section of the forest has been cut, moved to a new location. A general-purpose Soviet or Russian map would never show them, but a topo map would... giving one probably an exaggerated idea of an area's rail density, as in reality many of the lines shown would not be actually operational anymore (see (1), above). Anyway, by now, I suspect, most of these logging railway live on cartographers' desks, as the timber industry has mostly switched to using trucks.
A sugar cane railway, near Proserpine, Queensland, Australia
A somewhat similar class of railways are sugar-cane railways, which apparently are responsible for the extraordinary visible density of railways in Cuba, Mauritius, parts of Taiwan, and even a rail line in Fiji. I am not sure if the map shows the sugar railways of Queensland - I think if it did, there would be a more dense network there. The sugar railways are, like forest railways, narrow gauge (sometimes, very narrow gauge), and only used to move a particular type of cargo. Unlike many forest railways, sugar railways are permanent, even if used for only a few weeks in a year, to transport cut canes to the nearby sugar mill. Their existence is made economical by the fact that sugar cane's yield, in tons per hectare, are much higher than those of most other crops grown on similarly large scales. I know that at least some such systems in Queensland are still very much in operation, and I've seen tracks for one of them in Fiji (no idea if they are ever in use, though), but I don't know about other countries.
(3) Dr. Ranking contrasts the American (meaning, here, US, Canada, and Argentina) railway network to systems elsewhere, by justly noting that "In the Americas, rail was the primary route by which crops reached global markets, and railways and settlement often went hand in hand." This is true in a sense - the remarkable dense networks covering the fairly sparsely populated agricultural regions of the Great Plains of the US and western Canada, central Argentina, as well as the grain-growing areas of Australia's Victoria and Western Australia are quite remarkable. But one should not forget, at the same, how extraordinary and short-lived phenomenon these networks were. They were, basically, brought to life by the particular situation that obtained during several decades in the second half of the 19th century through the early 20th century: the railway technology was much more efficient for moving grain and other cargoes overland than any other option available (which, in those areas mostly meant a horse and a cart).
It seems that soon after trucks became widely available and the governments subsidized highway construction, the less-used 50% (sometimes 90%) of this unique rail network became abandoned. The system reverted to a form more "sustainable" in the truck-and-road based economy: railways connecting major transportation hubs, with trucks moving grain and containers to the surviving high-volume stations. If one were to wipe all disused railways from the US/Canada/Argentina/Australia maps, and add all new railways that have been built over the last several decades in countries like China or Iran, I feel that the overall density of the operational railways today's in North America won't be that difficult from the comparable population-density regions of eastern Europe and Asia (Russia, Turkey, Iran, north-western China). And it will be only natural for high-population-densities regions in India and China to soon surpass the US and Canada with respect to the railway network density.
In a sense, I wish very much that all those rail lines that have been abandoned or converted to bike trails became active railways again, and all kinds of factories, warehouses, and other businesses - even post offices - moved back to the trackside districts, where they could ship and receive their freight directly by rail... but this isn't going to happen unless a very radical change in the different modes' transportation costs occurs.
As a comparison, in the late-19th century Russian Empire, the need to carry export grain to the sea ports was also a major stimulus for the railway construction boom. But the country - not even its most fertile areas in south-western Russia and Ukraine - never acquired as dense a system as Iowa or Saskatchewan had for a few decades in the early 20th century. Partly this indeed must have had to do with the availability of capital and the general level of the development of the national economy, partly with the simple transportation economics: with lower crop yields per acre, and much higher local population densities, I suspect that the net amount of grain to be exported from any 100-square-miles region of Ukraine or the Saratov Governorate was rather smaller than from a similarly sized piece of Iowa. As a result, they have not had to abandon all that much of railway trackage, except for in a few areas where the construction was moved by "mining or manufacturing", as Dr. Rankin says, and where that mining (or, less commonly, manufacturing) is gone. Among the lines still shown on the map, an example of this is a large part of the branch that goes east from Apatity and Kirovsk in Russia's Kola Peninsula.