It's surprising that the singleton is there - from what I have read on altdevblogaday and other gamedev websites it seems that game developers have long since moved past that antipattern. Honestly, I wouldn't have re-iterated the GoF patterns at all: there is already plenty of literature covering them.
If you'd bothered to click through to that chapter, you'd have seen that it's actually a lengthy dissertation on why singletons are a bad idea, including seductive patterns that are actually singletons in disguise and a couple better alternatives for when global state is really unavoidable.
If you had actually read the article about the Singleton, you would have seen that it discourages its use and explains in great detail what's wrong with the pattern and why you should stay away from it.
+1 to this site for tackling this overused anti-pattern.
Otherwise, quite informative.