Why is Frequency Conversion Additive in Acoustics Beating, but Multiplicative in Heterodyning?
I initially suspect this is the result of being a non-LTI system, the
  system somehow contains a time-varying element, but I cannot identify
  it.
  
  On my second thought, it seems that [it] is only a human perception of
  the change in intensity of two frequencies, and it's not an actual
  frequency component created by a modulation process


If you consider the human ear as a part of the system then a modulation process is involved. If it wasn't we would not be able to hear the 'beat' frequency. 

In a perfectly linear medium any number of waves can coexist independently, and a time-invariant system is insensitive to instantaneous amplitude so 'beats' have no effect. But the human ear - like an rf 'mixer' or 'detector' - is nonlinear. 

The generic definition of 'mixer' is 'a machine used for mixing things together'. The mixing process may combine those things to make a different product (eg. cake mixer) or simply so they can be transported together (eg. mixed sweets). In audio equipment a 'mixer' is the name for a circuit that combines signals without distorting them - ie. an adder. In rf design it is the name for a circuit which combines signals with distortion, ie. a multiplier.