I can see the argument for intelligence being unlikely to develop with the Sqids' reproductive cycle. How does natural selection favor intelligence when the only ones who are old enough to display it are also sterile? (I believe it was stated that Sqids reproduce before being old enough to be called truly sentient; someone correct me if I'm wrong.)

But there are numerous ways that could actually happen. Intelligent adults are more capable of protecting and feeding their reproduction-capable nephews and nieces. The young Sqids could be favoring intelligent mates even though it's not directly advantageous to them (see the many, often arbitrary, ways animals select for mates on earth). Or they could still be benefiting from increased intelligence, just not as much as their older relatives, thus still causing natural selection to favor increased intelligence.