First, it gives quizzers check points and goals to achieve, breaking the memorizing into more easily accomplished pieces. Knowing that you have finished one of 10 or 16 chapters makes it clear that your making progress.
Second, it ensures that the quizzer actually knows the chapter they are quoting. Lots of times, a quizzer will come in and say they know a chapter, only to quiz pathetically over that chapter in practice. If they can quote it with four mistakes or less, you know they know it.
Third, it gives you something else to recognize. Obviously winning games and scoring awards are important measures of a quizzers ability. Some quizzers may not be high achievers on the buzzers, but by acknowledging the work they have done memorizing, you give them a goal they know they can hit. You also give them confidence, which can often lead them to scoring more points in matches. It also gives you something to recognize early in the year before competition starts.
Checking off chapters is a great way of helping quizzers get through the material. Make sure they keep reviewing after they check it off, otherwise they'll still forget it. A good rule of thumb is to quote everything you know twice a week. Also, remember that for the memorization awards quizzers have to quote to someone who isn't a family member.