i think we need to really look at this the other way around. Its not like Nvidia is being outdone by AMD more the obvious reverse.  So the op is asking the wrong question completely.  Its more correct this way:
Why does AMD have to price their cards so much lower than nvidia does? 
To answer this question is to solve the entire mystery. This that boggles the mind of the one responsible for the OP.  
The obvious answer: 
AMD prices their GPUs in a market they are competing in.  Currently even with their lower prices they are not selling as many GPUs as their competitor.  In the discrete market, Nvidia out sells AMD by about 2 cards to their 1. So we now see that AMD even with lower price is being out performed by Nvidia.  It is beyond debate, AMD has prices set according to what the market will pay. The lower price helps them sell cards.
Considering that nvidia holds nearly 2/3rds of the dGPU market, perhaps AMD should lower their prices even more.  Dont look at this backwards like the OP has.  AMD has lower prices because they want to sell cards.  
This is not unusual.