I'm having a hard time working out whether Khan just over simplified things in the video or he's just wrong. I'd have to say the latter, but the problem isn't in the z or t question. He's calling what he calculates a confidence interval and then says that he's 92% confident that the population mean falls within the given range. That's quite simply not something you conclude from a confidence interval... unfortunately.
So then I go back to the t vs. z question and start wondering if he made an error there. I'm thinking that perhaps not because he does state that if the sample is smaller you have to make a correction. So the other answerers are probably correct on that. He's just using z because he has already introduced it and it's close enough with the n of 36. I don't plan to go through all the videos but I'm imagining he'll introduce the t distribution later, hopefully the next one.
It's really unfortunate that Khan Academy is wrong on so many areas of stats... but maybe I just feel that way because I only get pointed toward videos with problems.