As a mathematician pointed out on the talk page, "guessing" a number from an infinite set is problematic. How, after all, could someone guess a number that requires 10^100 digits to express?
By that logic the dart example is also problematic because it's impossible to have a dart tip with exactly zero area, in practice it will always have a non-zero area. There's always a certain level of abstraction inherent in mathematics, hence why it includes more than just the small finite set of numbers which can be expressed in at most 1e100 digits.
Besides, the same can also be said about the third example, ie "but you can't really toss a coin an infinite number of times". Sorry but that particular objection just seems silly.
The dart example seems less problematic
True, but it also presupposes knowledge of geometry and the areas of various geometrical shapes, whereas literally anyone without any mathematical knowledge can follow "I'm thinking of a number, guess which one".
although I don't think it applies to "souls," which seem to be discrete entities
Why? If we're going along with this concept of souls of which there are an infinite number of potential ones, then why couldn't they be parameterized by, say, a countably infinite number of binary parameters? Which would make it equivalent to the last example on that wiki page (the "Tossing coins" one).
Discrete doesn't necessarily imply countable, it depends on the topology. For example any uncountable set under the discrete topology is trivially discrete. Then of course you wouldn't be able to define integration over such a set, so it wouldn't be much use in a probability space, but still it's not necessarily true that discrete implies countable.