Transmission Lines:Standaing Wave Voltage Characteristic at Half Wavelength
So I don't know how he can say that the characteristics repeat or maybe I'am missing something.

You're missing that he is talking about the 'characteristics' of the standing wave, and not the instantaneous voltage. He's talking about whether the amplitude of the standing wave has a peak or minimum, is at an antinode or a node, as you move along the line. That repeats at half a wavelength.
One of the reasons we study standing waves is that before modern equipment like VNAs, it has been the only measurement method we could use. In fact even these days, if we want to move into a higher frequency RF region where we haven't built a VNA yet, we're back using the old standing wave methods. The reason is that we can measure the amplitude of an RF signal with a very simple and wideband diode detector. When we combine that with a slotted line, we can plot how the standing wave changes with distance, and so calculate reflection coefficients. The ratio of the max and min amplitudes gives us the magnitude of the reflection, and we can infer its phase from the position of the max or min along the line.
As a diode detector simply measures the amplitude of the wave, not the instantaneous voltage, things repeat along the slotted line at λ/2, not at λ.