I find this a pretty confusing explanation because the actual mechanism is buried in the middle and you can't understand the first diagram without it.

The goal is to produce the number `0...010...0` with the same number of trailing zeroes as x.

If you flip all the bits in x, then `...10...0` turns into `...01...1`. Adding one cascades the tail into `...10...0`.

You can do this entirely in unsigned math and you don't need to drag two's complement into it. The fact that it corresponds to `x & -x` is a curiosity, and then you have to explain why it works for e.g. negative numbers, where it counts trailing ones instead but still produces a positive.

There are plenty of other tricks like this, e.g. `x & (x - 1) == 0` tells you if a (non-zero) x is a power of two, but it doesn't work for negatives.