He's actually wrong on the ABI requiring the top bits to be 0. It only requires that the bottom 32 bits match the parameter, but the top bits of a 32-bit parameter passed in a 64-bit register can be anything (at least on Linux).
The reason the code in his post works is because the upper 32 bits of the parameters going into an addition can't affect the low 32 bits of the result, and he's only storing the low 32 bits.
You can see that in this godbolt example: https://godbolt.org/z/M1ze74Gh6
The reason the code in his post works is because the upper 32 bits of the parameters going into an addition can't affect the low 32 bits of the result, and he's only storing the low 32 bits.