Need help understanding 16QAM constellation diagram
Yes and no.

The mapping is arbitrary as long as the receiver correctly determines which constellation point a symbol is.  If the receiver makes a mistake, though, it is most likely going to pick a "neighbor" constellation point (i.e. a constellation point that is only one spot away).  It is highly unlikely that a correctly implemented receiver will pick a constellation point far away from the transmitted point.  Communication systems try to mitigate the impact of the "neighbor" mistakes by minimizing the Hamming distance between neighbors.  A map where all of the nearest neighbors have a Hamming distance of 1 is called a Gray map.  If you use a Gray map almost all of the symbol errors will only result in one bit error.