Sorry that you didn't feel this post hit the right balance between too much versus not enough detail! 

The straightest answer I can give you for why NM had "the driest El Niño on record" is that...it didn't. 

New Mexico and many parts of the southern tier of the US did see the typical El Niño impact of a wetter-than-average winter. In terms of ranks, it was not the wettest El Niño winter for NM, but it also wasn't the driest. I didn't have to look very far back in the history to find out that the winter of 2018-19 (also an El Niño winter; you can find the list of historical episodes here) was drier than this past winter. 

Now, as far as a brief summary of what this post is about, this is how I would put it: 

• This winter's precip forecast appears to be the result of at least two influences interacting with each other: (1) El Niño and (2) the long-term trends in sea surface temperatures in the tropical Pacific Ocean (warming the west and cooling in the east). 
  • This interaction intensified the level of dryness forecast for the PacNW (because both El Niño and the trend favored dryness).
  • This interaction weakened the dryness forecast for the Ohio Valley & Midwest (because El Niño favored dryness but the long-term SST trend favored wetness in places).
  • This interaction weakened the level of wetness forecasted for the southern tier (because El Niño was pushing things toward a wet winter, but the trend was pushing it toward a dry winter.)
     

Hope this helps!