Is there something wrong with the following sentence: "reader who tries to figure it out as they read."

[christophe]

Hello all,
I read this sentence and I wander if there's a mistake:
"The relationship between games and detective stories has been established by Suits (1985), who argued that detective stories created a game-like relationship between the author posing the mystery and the reader who tries to figure it out as they read."
Reader = they?
The correct sentence wouldn't be "reader who tries to figure it out as she read"?

I found a similar sentence latter in the same text:
"if the player has seen the film or read the novel, they would probably know the solution to the mystery already, rendering the efforts of the player/detective irrelevant."

Christophe

[Alan]

Yes, strictly speaking it should be '(s)he'. 'They', however, is commonly substituted - nowadays even in written English - to refer to an indefinite pronoun.