You can find a lot of motivation for 128-bit integers in that paper, such as fixed-point operations, implementing 128-bit (decimal) floating-point, financial calculations, cryptography, etc. However, the proposal has been superseded by P3666, which aims to bring C23's _BitInt type to C++, which wouldn't just allow for 128-bit integers (as _BitInt(128)) but for any other width as well.
You can find a lot of motivation for 128-bit integers in that paper, such as fixed-point operations, implementing 128-bit (decimal) floating-point, financial calculations, cryptography, etc. However, the proposal has been superseded by P3666, which aims to bring C23's _BitInt type to C++, which wouldn't just allow for 128-bit integers (as _BitInt(128)) but for any other width as well.