What makes a scorer pure? Well, by our standard definition of purity, it'd be the absence of all that is not scoring. So that would mean assists, and if you wanted to stretch it out, also perhaps rebounding and defense. In the end, by defining the "pure scorer" in this way, you're also defining the "one-dimensional ballhog." That doesn't sound as nice, does it? We'll leave it focused on offense for ease. Points will represent the pure, and assists and offensive rebounds will represent the impure.
Setting aside the question of whether it's even a good thing to be called a pure scorer that Ziller addresses in the article - that you should check out before reading on here - a couple of Golden State Warriors were mentioned and Klay Thompson ended up being at the top of that list. The top five were as follows (along with Stephen Curry's numbers for reference):
2012-13 for the purest players (and Stephen Curry) on the "scoring purity scale".
** League-high among perimeter players
So to be clear, Ziller isn't necessarily saying Thompson is either the NBA's best scorer or shooter - he's saying Thompson is the player whose offensive tendencies are skewed most heavily toward scoring without regard for shot volume or efficiency. I included the per minute stats in the table above to help illustrate why Thompson is so "pure": he recorded very few assists or rebounds last season, the lowest on this short list (and the effect continues to get more stark as you go down the list). In contrast, Curry's tendency to pick up assists puts him on the "impure" side of the index (along with LeBron James and DeMarcus Cousins).
Obviously, this framework doesn't take defense into account as Thompson emerged as a key defensive presence for the Warriors and Anthony...wasn't that for the New York Knicks. And it doesn't necessarily lead us any closer to answering the question of who the best scorer is: while almost anyone would probably prefer Kevin Durant's balance of purity, usage, and efficiency that makes him almost impossible to defend, we probably didn't need this scale to tell us that (although it does make Durant's value in the league even more clear when compared to other players we might consider pure scorers).
Ultimately, without adding some sort of measure of quality (e.g. efficiency?, range?, scoring creativity/versatility?) it's hard to take much from this scale - understanding a given player's style of play can be extremely helpful in building a roster, but it can still be difficult to figure out how valuable a pure scorer is to a team. For example, an argument could easily be made that a moderately efficiency pure scorer who gets less than one trip per game to the free throw line (Thompson had 1.9 FTAs per game last season) isn't worth a whole lot, but Thompson's ability to stretch the court with 3-point shooting and contain perimeter threats defensively were clearly valuable to the Warriors' success last season.
Yet Ziller's point in doing this exercise was actually something I'm quite sympathetic to: people really do toss around these terms arbitrarily to the point that the words lose their meaning altogether. And ultimately words do mean something.