PaulP: "So, which is a better ENSO model? Mine or this ML version?"
Let measured predictive success decide the question. I agree with you below.
PaulP on ML Version: "a great addition to open-source climate science. "
Caution: Machine Learning is also susceptible to overfitting and underfitting, caused by imperfect data.
Here is NOAA prediction as reference-model. They seem to avoid overfitting and underfitting risk better than simple models dependent on narrower data-sets.