I've been awake the whole night and have things to be doing later in the day so I hope you don't mind if my reply is largely unsourced. I'm going to lean off of memory and my classes a little.
Chinese warships have been playing chicken with United States vessels for a long time, but I'm not convinced that those two incidents you linked mean anything. The Chinese navy did, of course, not sink the vessels in either of the incidents you've listed but nor did they threaten to sink or fire upon the American vessel or plane if they continued further. This is important because it ties into the international relations concept of "cheap talk" -- you can saber rattle all you want and be threatening all you want but it means nothing if a credible commitment is not made, a promise of action on which political capital lies. China has not made a credible commitment in regards to American vessels in the South China Sea, it's just been as aggressively there as it can because it wants to send a message to the weaker nations that its presence is not gone.
Playing chicken with US vessels and trying to chase off US planes are not a cause of worry the way they are being conducted.
China is also not Argentina, it's true, but the US isn't the United Kingdom either. China pursues a rapid increase of technology with its navy, but it hasn't accomplished it and I doubt it will for at least a couple of decades -- their carrier, for example, is not particularly deployable and certainly doesn't have the same capacities that American ones do. For all the Chinese Navy works on fortification and missiles, they do not have the power projection that is actually necessary in order to prosecute a war, and the United States has a level of power projection capacity in sea and air that the British were never capable of.
The Chinese navy has lots of ships, but it doesn't have a lot of ships capable of actually launching a fleet level battle -- it has subs, some of them nuclear but really not that many. It has a lot of destroyers and frigates and corvettes, but very little larger than that. It has one active aircraft carrier of poor quality and another one it's working on, while the US has anywhere from 11-17 depending on how you're counting aircraft carriers. The Chinese Navy DOES have a technological gap to work on, and of course it's working on closing it, it has every reason to do so. But that doesn't mean that it's reached that gap, and it doesn't mean that it's about to soon, especially since it's not like the United States is sitting around doing no research.
China also has every reason to brag about its supposed ability to challenge the United States Navy because it actively will want other actors (including those within China!) to believe it can do so, because it will change the way they act about it. This gets repeated in articles like the ones you linked that claim the Chinese Navy as a serious contender to trouble the USN, which go off of Chinese military sites and Chinese political statements themselves; this does not actually mean that they possess this capacity. EVERYTHING in international relations happens for a reason, and this extends to the statements governments make and the way they make them. Is it a coincidence that that Chinese jet was spotted when Trump was meeting with Jinping? Is it coincidence that much of the meat of that NYT article comes from Chinese statement? It is not.
The Chinese Navy is not built to perform large scale, anti-fleet operations when you get down to its composition, and China spends a much, much smaller portion of its money on the navy than it could; this is because the Chinese do not WANT to perform large-scale, anti-fleet operations. The Chinese don't even right now want to build to the point of doing so. China knows that it would lose such a conflict, and because in addition to not being Argentina China is also not Nasser's Egypt they have been avoiding presenting a threat in concrete enough terms to actually spur action from the American military. China wants to be seen as capable of prosecuting a war by its neighbors and its politicians, China doesn't want to actually be capable enough of prosecuting a war to start one -- it is very much restrained in its military burden, economically, and I fully believe that China could manufacture a far more heavyweight navy than it has now.
But it would still have the technological disadvantage, it would still lose, and more importantly it would take a lot of damage to its economy and a lot of damage to its overall international strategy that would far outweigh whatever deterrence it would hope to get from a conflict over the South China Sea. The PRC is trying NOT to become a pariah state, it is trying to form a stable sphere of influence internationally and primarily through economic means, like the actions it is taking in Africa. That's why its alleged military strength comes out mostly in words and is a public presentation rather than an actual gathering of naval forces like the kind that starts unintended wars like the Six Day War. China has more to gain from talking about the South China Sea and appearing interested in engaged than it actually does from committing to driving the US off, and it certainly has much less to lose. China also knows this.