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That's what makes it a fighting game.
The term obviously has no 'real' meaning in that sense, right? I'm not gonna argue 'all games that contain fighting are fighting games'.
That means there must be a definition of 'fighting game' that goes beyond 'a game where people fight', and some subset of Action Games are 'fighting games', because almost all Fighters are 'Action Games'.
By the definitions that are generally accepted for 'Fighting Game', BNS is one. You just described one that is unfortunately almost fundamental to the genre definition. Even the definition of Combo is as expected.
"Your first strike put your opponent in a state where it was not possible to recover in a way that allows them to avoid the next strike." - basic definition of a Combo in the form required for fighters, which is exactly how it works in BNS.
Either way I guess your response is moreso a 'proof indicator' than anything else. We don't bring up BNS because 'people don't want fighting games' in their MMOs, some people may not understand 'which is which' but they're pretty set on their perception of what they do and don't want, so it isn't really possible to advance the conversation.