I see that this is a direct cut-and-paste from the article, so you haven't left out anything that would make these statements more understandable. First, what does "integrity at the elbow joint" actually mean, and how is this affected by the use of dumbbells vs. barbells? This is not explained, and I don't understand.
Then, the statement "dumbbell pressing is cool because it encourages more stability at the shoulder and makes each side 'pull its own weight,' so to speak" implies that a barbell does not encourage sufficient shoulder stability, which is odd because I've seen raw 600-pound benches and I didn't notice any shoulder instability. And I haven't noticed any shoulder instability in the rather common 400-pound benches either. We have all watched the video of Serge Redding pressing 502, with a breathtaking lack of instability. I teach barbell training to people all over the country all year, and one of the very first things we teach is HOW TO BE STABLE UNDER THE BAR, one of the many responsibilities of the coach. Everyone seems to learn this pretty well, and then they go home and work on it some more. On the other hand, I haven't ever seen a pair of 300-pound dumbbells benched, and I guess maybe the fact that they'd be catastrophically unstable might be a factor. As for each side pulling its own weight, barbells tend to do this as well. When you don't, the bar becomes "uneven" or "not level", something even a lay person can detect, and the first thing a coach would address.
This: "But all that aside, the ability to play with the elbow in turn affects the position the shoulder is in at the time we press." is okay, if not a bit cryptic. But the following statement: "It would be a wise move – especially if you fall into an acromion category discussed above – to slip into a grip (using dumbbells) that's closer to neutral when performing your dumbbell bench and overhead pressing." implies that the inability of the wrist to supinate a little with a barbell has something to do with the position of abduction of the shoulder. A moment's reflection upon the differences in abduction evidenced by shirted powerlifters vs. the elbow position we advocate would cause you to conclude that wrist position and humeral abduction are separate, non-dependent variables. Or maybe I don't understand the point, because "neutral" hasn't been defined in this context. I can stand with dumbbells in my hands and vary my forearm position from full supination to full pronation with only about 20 degrees of humeral ab/adduction variation.
"This way the shoulder can roll back farther behind the clavicle where it belongs and save you from unwanted joint pain." Somebody's going to have to explain what this means, because I have no idea how "the shoulder" gets behind the clavicle, or why "it belongs" there.
"The bar path isn't fixed either. Finishing with a narrower grip while neutral can also encourage more arm activation, especially depending on the kind of press you're doing." I have no idea what this means because, again, it's cryptic. It doesn't actually mean anything definite. Now, it might mean that he thinks the "bar path" -- we're using dumbbells, right? -- can converge towards the top, IOW the dumbbells can be closer together at lockout than they are at the bottom. They have to be, because each dumbbell must balance above each shoulder joint at the top, and each dumbbell must be a little wider than this at the bottom due to the length of the humerus and the need to keep forearms vertical throughout the motion. "Arm activation" is not really a technical term, so I'm not prepared to interpret it.
But this is the nugget: "Needless to say, if I were to choose one kind of pressing for life, I'd be on board with dumbbell pressing." This is just fine if all you want to do is exercise. Just come in the gym and mess around with some pushups and dumbbells and do some movements that make you sweaty, tired, and maybe even sore. But this is not training, and we train -- we don't exercise. As I have discussed many times, dumbbells are wonderful for assistance work, but they do not lend themselves to being trained, for reasons you can look up on this board.