No it doesn't.What they have actually written clearly says that the feat as a whole applies if they provide a feat bonus to hit or damage.
The phrase is not "the feat as whole applies". The phrase is "the feat applies". The words are silent on whether "the feat" here refers to "the feat as a whole" or "the feat in respect of the feat bonuses to hit and damage that it confers".
Another anology: I get up, check the fridge and say "There's no milk". Do I mean "there's no milk anywhere in the universe" or "there's no milk in our house" or even "there's no milk in our fridge"? The words uttered can bear any of those meanings. But no would interpret me as meaning the first. And it's very likely that I mean the last.
What is written is "the feat applies". It leaves it as an open question the extent or nature of that application.Which is nothing like what was actually written.
Actually, I don't think law is a particularly good example to support the (in my view spurious) notion of RAW at all. There is no serious judge or academic that I'm aware of who things that because a phrase appears in a statute or contract without qualification, it therefore goes without saying that it is to be interpreted as unqualified. Even the most hardcore textualist will accept that the text must be read in a context, which may suggest a qualification.Law is actually a great example of this, as no matter what you believe about a particular law, short of a Court actually validating that belief in a specific case, it isn't true in a legal sense.
Game rules are no different. Furthermore, it would be absurd to expect the rules for D&D to be written with anything like the same precision as legal instruments, given that the amount of money and resources thrown at D&D rules every year would presumably not be enough even to run the courts and legislatures of Tasmania or Vermont for the same period. This speaks even more in favour of resolving doubts (including doubts as to an intended but not express qualification) in favour of what everyone believes the balanced intention to be.