An important dimension missing in this type of map is cost of travel. If you are willing to spend sufficient money, my guess would be you could reach pretty much any spot of land on earth within about 48 hours, with the appropriate combination of helicopter and private jet... But if you limit yourself to, say, 2000 Euros, you could probably make it to many places, but it would take significantly longer.
It's a great point for people who want to recreate a modern version of this map, but for 1914 I think "anywhere at any cost" is still an interesting yard-stick.
More relevant nowadays, due to the ubiquitous nature of transportation, I suspect would be seeing a map that charts not time necessary to reach a location (after all 72-96 hours would cover the overwhelming majority of the globe) from a given starting point but rather the nominal cost associated with doing so.
You'd have to define "pretty much." It's probably less than you think in terms of total landmass. There are countries and areas within countries that are restricted in various ways. There are also rugged remote areas that aren't suitable for helicopters and islands lacking airstrips.
