Unfortunately, his simple explanation of these concepts is just not correct. He claims functors are a container you can map on and that monads are also containers.

Here's a monad (which is also an applicative functor) that isn't a container: probability. The space of probability distributions is a functor which can be mapped. In the sampling representation:

    p.map(f) = new Prob {
      def draw = f(p.draw)
    }

It also supports flatmap:

    p.flatMap(f) = new Prob {
      def draw = f(p.draw).draw
    }

Yet nothing is "contained". Each Prob object is just a random number variable generator.