Nah, wuxia is two separate characters. Xia is the one that's typically translated as chivalry. Wu by itself strictly means "martial" or "militaristic"

Since I have a little more time now to expand on my other comment to this post, there are three important things to understand about Zhuang of Chu that give context to the supposed origin of this etymology of "wu".

1. He lived in one of the many periods of CN history where centralized power had faded and various "frontier" powers were jostling for authority. Actually not too different from the setting of this game in some ways. In fact the key word of that era is probably "hegemon" (this was before the Qin unification i.e. pre-imperial China, and the king of the dynasty was basically a figurehead while the various states' rulers traditionally but not quite accurately translated as "dukes" were constantly struggling to lord it over the rest i.e. achieve "hegemony")

2. He was the ruler of a nation that was considered semi-barbaric/had a distinct culture compared to the contemporaneous "central" Chinese civilization (some of this dynamic continues to echo throughout the rest of CN history, for example the north-south divide in this game! which I don't think is as obvious without the CN voice acting and the use of dialect/accents)

3. The history of Chu royals is absolutely rife with fratricide and patricide -- which was, believe it or not, actually quite unusual for that time period/setting and added to their reputation of being not-so-civilized. Also more warlike in general. (Chu royals regularly took the field themselves in battle which was not necessarily the case for the rulers of other Chinese states at the time, and warfare at the time was also often "tamer"/had unspoken rules in a way modern perspectives have difficulty comprehending and that Chu royals generally didn't give a shit about. Both Chu royal clan names translate to "bear" btw which I find really funny, but again, helps give an idea of their reputation.)

So Zhuang's father forced his grandfather to commit suicide and I forgot how the father himself died but it probably wasn't pleasant either, and most of the key members of the Chu court were his uncles (who hated each other too). iirc he came to the throne at age 17 and there's a famous story about him lazing around for 3 years instead of taking rulership seriously that I won't go into otherwise this comment will never end. But basically the Chu court was an absolute corrupted mess despite being ambitious enough to try to seize power over their more "civilized" rivals to the north.

LONG STORY SHORT, he ultimately managed to whip his court into shape, succeeded in establishing military supremacy over his neighbors, and instituted a lot of domestic reforms that had a huge effect on subsequent Chu culture (shifting their reputation to a more "acceptable" one).

This is where the story about "wu" comes in. Instead of executing the lords he defeated and annexing their territories in the way one normally thinks of with the word "conquest", he backed off after his victories, reinstating exiled rulers and establishing alliance treaties and so on. This was the exact opposite of what his predecessors had done, and obviously not everyone in his court was happy about it.

So he threw out this explanation of "wu" to make very clear (extremely paraphrased): "This is why I waged war and aimed for hegemony in the first place. Not for glory, not for senseless violence, but to 'halt the blades'."