The musicians who played on the album are mostly Brian's band, with a few Joe Thomas ringers, and David on guitar. Doubt if any of the other Beach Boys play a note, unless Brian taps the keys a little.
... not even a little rhythm guitar here and there by a certain Jardine?
Why would he be playing? He's not an especially good guitarist, as I'm sure he'd admit himself (he's not *bad*, but nor is he particularly proficient), and if they wanted a guitar part Scott Bennett, Scott Totten, Nick Walusko, Probyn Gregory, Jeff Foskett, David Marks and whoever Thomas' session musicians are were all available, almost all of whom are far better on the instrument.
Given the songwriting and production credits, I strongly suspect that Brian was the only Beach Boy to attend any of the tracking sessions, except for those sessions that David played on (and Daybreak, presumably).
Al is actually a really great guitar player. I saw a show around 2003 or so and he played all the solos and nailed 'em -- I was blown away. Not sure what was up with that clip ... I think he's just kind of meticulous and was unprepared or something.