One needs to look at the overall pattern of correlations in the PACF plot instead of the correlation at a specific lag.

For example:

In the two PACF plots illustrated in the article, one needs to look at the strengths of correlations at lags that are multiples of Lag-2 or Lag-12.

In the PACF plot , if you see the correlations dropping off sharply after Lag 2 (in case of the PACF of the southern oscillations time series, we do so), it indicates an AR(2) signature, In this case, it does indicate a seasonal period of 2.

If instead, one sees correlations gradually tapering off at lags which are multiples of 2 (lag-4, lag-6, Lag-8 etc), it indicates a seasonal pattern of period 2.

This slowly decaying pattern is evident in the PACF plot of the average monthly temperatures time series at lags 12, 24, 36 etc. indicating a seasonal period of 12 in the underlying time series.

I hope it's clear now.