If a problem is NP complete then there is an algorithm to solve it in nondeterminstic polynomial time. Any nondet algorithm can be transformed to an exp poly time algorithm (just run through each of your poly time algorithms one by one) so showing CLIQUE has an exp algorithm doesn't help at all. We want a lower bound.
No, he is claiming that l-CLIQUE requires exponential circuit size (this is the reason that most of the proof talks about circuit complexity and not time bounded Turing Machines). This is not necessarily the same thing as exponential time.
