I said it's not exactly "maximal" training. The words I use are very purposeful
It is not maximal training at least not in the way that I mean. "Strength training" is a much more general term and can mean all sorts of things. There are too many different strength qualities to define "pure strength work" And even absolute strength can be effected with other parameters than just maximal intensity work.
You can call anything strength traing depending on how it relates to your needs and goals. And you can call some things more "maximal" than others. But my philosophy when it comes to maximal work is that which involves intensity over volume. While 3x3 is heavier than 5x3 is heavier than 3x5 is heavier than 5x5 they are all related in a quantity first aspect.
But no, am not using the term pure strength but maximal training. And certainly warming up to a series of singles, doubles, or triples, would be in my view maximal training but of course there are other ways.
I have said before that many people use "intensity" as a catch-phrase more than anything else. They say intensity is important but their training doesn't reflect that. Becasue if intensity IS the most important criteria for the development of absolute strength then it is REGARDLESS of any other parameter we associate with resistance training. So, in that view, 3x3 is not viewing intensity as the sole most important parameter. In that setup, 9 reps in three sets is as important as weight on the bar. So intensity is only given importance in relation to volume.
That could mean a lot of things to a lot of people. Keeping aside how your would approach such things on a continuing basis (just viewing one workout in a vacuumn) it may mean that working up to your heaviest set of 3 could be more useful than your "3x3". OR, does this intensity relationship mean "heaviest"? I say certainly not unless you want to lift like crap all the time.
So another aspect of it that is very important to me is the notion of quality over quantity. How many quality reps can you do at a given intensity? And lets supposed that intensity is at least 85% or above and spending plenty of quality time in the 90% or above range.