For the very first exercise listed (decline bench on page 4) it states:
The last set you will go to failure
Even if the article didn't say that, I would personally never recommend going to total concentric failure on each set as you would fatigue very quickly and really tax the CNS.
The first few exercises are (12,10,12) in terms of rep recommendations. I would think that either means holding something back for the last set or lowering the weight slightly on the last set to get the additional reps.
This is a high volume routine and thus you have to be very careful with failure.
I would define failure as when your speed slows down significantly. You should not be grinding out reps to get to the prescribed number of reps or in an attempt to reach total concentric failure.
On the last set though, continue until you have a really slow rep and consider that your point of failure.
I hope that helps!
James 1:16-17 ESV
Do not be deceived, my beloved brothers. Every good gift and every perfect gift is from above, coming down from the Father of lights
With God's help...Mens sana in corpore sano