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.
The LLVM x86-64 ABI requires the top bits to be zero. GCC treats them as undefined. Until a recent clarification, the x86-64 psABI made the upper bits undefined by omission only, which is why I think most people followed the GCC interpretation.
In theory. In practice the vast majority of Linux userland programs are compiled with GCC so unless GCC did something particularly braindead they are unlikely to break compatibility with that and so it's the ABI everyone needs to target. Which is also what happened in this case: The standard was updated to mandate the GCC behavior.
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.