Thought you were referring to the angularity of the plot lines -- the data is only monthly sampled so the connecting lines are not smooth. The parallelogram shape is a hysteresis lag effect as described in the link. This will be seen in typical lissajous patterns
The multidecadal cycles that Michael Mann thinks are phantoms likely come about from the closeness of the the strongest tides Mf and Mm, which have values when aliased against the annual cycle of 3.8 years and 3.9 years. This creates a longer term beat cycle, which is the aliased Mt cycle in which ~40 cycles fit into a year. It's not exactly 40, but about 39.99 which means that the strength of the Mt tide on the annual impulse only gradually changes from year to year, giving rise to the multidecadal character of AMO. ENSO doesn't have that character, likely because Mf is incrementally stronger.
see the comment after the blog post: https://geoenergymath.com/2020/12/22/overfittingcross-validation-enso%e2%86%92amo/#comment-2245
when the aliased Mm approaches aliased Mf then the slow modulation gets stronger