When reading about any predictive technique the first thing to focus on before trying to understand the predictive mechanism is to understand the predictive accuracy of the model. A paper like this should have extensive discussions of overfitting, underfitting and overall predictive accuracy. The entirety of this paper's attempt to address this is:

"Last, to avoid arbitrary fitting and to obtain a robust measure of forecast skill, we apply a fourfold cross-validation scheme for each model: the model is fit to three-fourths of the data to predict the remaining one-fourth out-of-sample, and the procedure is repeated for each one-fourth segment of the time series."

They are dealing with time series data, which naturally has temporally correlated observations so a cross-validation like this will give a biased error estimate that will favor the more complex model (it encourages overfitting). I haven't delved into the details, but compared to the Ricker model their model is likely more complex so I have very little confidence in their claims of accuracy.

Of course, the choice of the Ricker model (developed in the 1950's) is really a strawman in any case. There are much better competitive techniques they could have chosen to benchmark their work.