The language pattern the author refers to is called litotes (https://en.wikipedia.org/wiki/Litotes), but to say that English doesn’t use them is… not quite right.
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If I'm understanding the author's account of Chinese assertion-by-negation correctly, doesn't it sound like assertion-by-negation is the ordinary case in that linguistic tradition, and it's the assertive case that jars the ear? Same pattern, different effect?
No? Assertion by assertion is the ordinary case, just like you'd expect for everything.
But it's easy to say 他没猜错, because it takes advantage of a common element of Chinese grammar that doesn't match well to English.
Think of 猜错 as a verb with an inherently negative polarity, like "fail" or "miss". There is no difficulty in saying "he didn't miss", even though there is difficulty in saying "he didn't not hit" and missing is always the same thing as not hitting. 猜错 is similarly easy to use. (Though it's less opaque; it is composed of the verb 猜 "guess" and the verbal result complement 错 "wrong".)
The opposite of 猜错 is 猜对 ("guess right"), and it's very common.