The box shown is just assembled with sticky tape.

A similar way would be to get a box that is over-size, cut it in 3 directions, into 8 sections (with one corner in each section) and reassemble it with the parts overlapping. The cardboard doesn't need re-folding, and suffers no strength loss because of it.

Leaving the last two sections to re-assemble. The completed box has all the original edges and corners intact. This is absolutely different to the video, where the guy cuts along the original edges. But it does need very good sticky tape, on both sides of every join.

The box shown in the linked video was just assembled with sticky tape.

A similar way would be to get a box that is over-size, cut it in 3 directions, into 8 sections (with one corner in each section) and reassemble it with the parts overlapping. The cardboard doesn't need re-folding, and suffers no strength loss because of it.

Leaving the last two sections to re-assemble. The completed box has all the original edges and corners intact. This is absolutely different to the video, where the guy cuts along the original edges. But it does need very good sticky tape, on both sides of every join.

Of course, if the box is already the right length in any direction, it doesn't need to be halved that way.