The "rule by law" philosophical approach is a practice that is borne out in China's imperial past and is as much a historical worldview of "rule of law" as in western society. The generalization is on purpose to highlight the underlying philosophical thought of governing in Chinese culture. The SCS is an example to demonstrate such a concept in action. You are free to disagree and I respect your disagreement. It is an opinion but I have taken the effort to lay out the basis of such a view.
I disagree that such a dramatic supposed divergence in philosophy exists, and I especially dispute the existence of such a divergence in philosophy regarding the way China and other nations behave on the global stage, because you are assuming that the way China is currently acting in a very specific situation (SCS) is reflective of how it always acts, despite ignoring all the vast majority of situations where China's actions on the world stage are perfectly legitimate.
I also am not very happy with the way you are using the word "culture". Despite being Chinese myself, I appreciate that I have very limited understanding of the long and complex history of China's culture to governance (though not for a lack of trying), and I think if one wants to try and draw any kind of parallels of China today and China's past practices would require an understanding of both China's actions today and China's history.
Now, I do not understand China's history and whatever cultural tradition of governance as extensively as I should, and I would argue that you probably do not understand it well enough to claim that such a specific and particular philosophy (of "rule by law") existed in the exact form you describe to such an extent that it could be described as "underlying philosophical thought" -- however we are able to appreciate China's current actions on the world stage, which I think we are both able to perceive. And thus, when we go about this basis of assessing China's actions on the world stage, I think it's fair to say that there are only very few limited, specific and unique situations when China's actions could be considered to be "rule by law" like how you describe, thus I believe your original position about imperialism of whatever when China is the head of a new world order is flawed.
In short, your claim is too ambitious and not supported by sufficient premises or evidence. I will offer an alternative claim in the second part of my post which I think is more logical and easier to defend.
The main difference in philosophy between "rule by law" and rule of law" is that the former sees "law" as merely an instrument to govern and is subservient to the one who wields it. In other words, it is an instrument of convenience subject to choice of application and interpretation with no constant in meaning and usage. In western concept of "rule of law", the laws are a constant and becomes a constrain to any governing body. No one is above it and application and meaning are consistent.
In the SCS example, China is selective in which part of UNCLOS it wishes to follow and just ignore those it doesn't like. UNCLOS provision is clear that the tribunal's decisions are final and binding and yet China says it will not abide by it. UNCLOS is clear on the meaning of innocent passage and yet China continues to push an interpretation that it prefers. These are all examples of a philosophical view of "rule by law".
If you said that in the SCS situation China was doing "rule by law" or whatever it is you're calling it, then I wouldn't disagree with you as much [edit: the problem is your generalization]. As to the tribunal, I should again emphasize that China is not the first nation to reject the ICJ's rulings. China has also made it clear that its territorial claims predate UNCLOS and are not bound by it -- this is called trying to interpret the situation in the best way for their own self interests.
The problem is that you are using a very unique situation and generalizing it to believe that this is how China would act in every situation in its dealings on the international stage in future in a potential new world order. That is the kind of illogical generalization which I simply cannot agree with, as the burden of evidence for such a large claim must be far greater than merely how China acts in the SCS dispute, which is a very unique situation.
[This part is the alternative claim I mentioned earlier:]
At best, you can argue that the SCS situation shows that China in future may be willing to contest certain international norms in future in situations which it perceives as vital to its strategic interests, if it feels like that is the only way to protect those interests -- that is quite different to laying out broad strokes that when China is the head of a new world order it would seek to carry out "imperialistic practices" to "take the rest of Asia and the rest of the world".
Trying to use the SCS situation to argue that it is somehow reflective of underlying Chinese philosophy towards governing is an even bigger claim that would require even more evidence as well... and I've already described in the earlier part of my post as to why I think such a claim based off the current evidence we have of China's overall behaviour on the world stage and the current (lack of) understanding of Chinese culture and governance in its long history and how it may relate to its present basis of international relations, is fundamentally logically flawed.
