It's really going to depend on what you're used to, and also what you run on your homescreens. Besides obvious stutters, a lot of "lag" is perceived based on what you're used to and what you "feel" when you're interacting with a device. So while we see a video and see no lag, it's possible the user is "feeling" it, whether legitimately or not.
That said, If you have any sort of animated or high-graphic widgets, it will occasionally stutter. If you're coming from the HTC One or iPhone 5, you'll probably notice it just feels like it can't quite keep up every now and then. Overall I felt the HTC One was indeed more responsive to my inputs, but HTC also has the animations ramped up pretty fast by default, which adds to making it feel faster. If you speed up the S4's animations in the dev options, it helps it to feel more on par with the One.
On the T-Mobile S4, the first iteration was actually very laggy, but after its first software update, it was greatly improved. So I have no doubt that any lag felt on the S4 is strictly due to software "interference". Whether or not they can tweak it to perfection (or want to take the time), who knows.
All in all, I would say my overall positive experience with the S4 trumps any occasional lag I might feel on it. Oh, and I wasn't able to watch the full video or hear him talk, but I did watch the part at 3:35 compared to the One.