..is, indirectly, trying to get more information about Lizzy's intellectual accomplishments, after hearing her intriguingly vague comment about not being a great reader, while at the same time her action is to grab a book and read rather than play cards. He's challenging her, as if to say, "you seem really smart, but I want to know if you are really as smart as you seem. show me some conventional evidence of learning, boast to me about the books you've read." But Lizzy is too clever, she neatly sidesteps this thrust by him, and instead, as Adrian just argued, she demonstrates her quick wit by her (devil's) advocacy of the position that Darcy demands too much. In that same moment, I believe Lizzy IS impressed by HIS formidable intellectual prowess and erudition.
They are like two heavyweight boxers in the second round of a fight, testing each other out, probing for strengths and weaknesses. And all of it implied, beautifully.