Well, it was my answer you're referring to so I'll explain.
The original question, in the link you provided, examined the Hadcrut4 data which shows temperatures from 1850 to the present day. This set of data shows global average temperature per month. What the original questioner did was smooth that data in such a way as to highlight a 60 year cycle. When combining this 60 year 'cycle' with a rising trend in temperature, you get a reasonable fit to the data.
What I argued was that if you take this dataset, which shows temperature as a function of time, and perform an analysis on it to examine the cyclical patterns in it (a Fourier Transform which gives you a graph of amplitude of cycle versus frequency or period) you don't get an appreciable spike in the 'spectrum' with a 30 or 60 year cyclical time. Therefore, you cannot claim on the basis of a direct analysis of the Hadcrut4 data that it contains evidence of a 60 year cycle.
How does this statement square with the PDO? Well, the following graph shows the PDO index from Jan 1900 to Jan 2017:
What you can see is that there's a period from 1900 to 1940 where the PDO index flips high and low but is mostly high. There's a period from about 1940 to 1980 where the index is low. There's a bit from 1980 to 2000 where it's high again, but then goes low for a couple of years, then high, then low, then high. The point is, what you have here is not some nice uniform 60 year cycle. What you have is a spiky mess with highs and lows. Sometimes it looks like an almost 80 year cycle. Sometimes it's shorter. So the point is that taking the Hadcrut data and smoothing it so you get what looks like a 60 year cycle, and then claim that 60 year cycle is due to the PDO isn't correct. It's not as nice as that. Hence you don't see the 60 year spike in the Fourier Transform. It's not regular. It has different periods.
The second issue is how does the PDO affect global temperature? Remember, the original Hadcrut4 data shows global averages. What we know is that the PDO index is not always directly correlated with temperature. For example, we know that temperatures are positively correlated with PDO index over western North America, mid-latitude central and eastern Asia, and central and northern Australia. However, the correlation is negative over northeastern North America, northeastern South America, southeastern Europe, and northern India.
So, the PDO isn't a nice regular 60 year cycle and some regions are warmer during high PDO index and some are colder. Why would you subsequently expect the Hadcrut4 data to show you a nice 60 year cycle due to the PDO if it's based on averages?
I'm not denying the existence of the PDO or it's impact on our climate over decade-length timescales. All I argued was that you can't take the Hadcrut4 data, smooth it to give you a 60 year cycle because it looks nice, and then subsequently say the 'shape of the smoothed data is due to the PDO because I want the PDO to be a 60 year cycle in the average global data'! Which appears to be your argument ...