(I don't understand the second quote so can't comment on it.)
One of my favorite poems is Be Drunk[0]. Would you take someone agreeing with the "thesis" of Be Drunk (thinking it's necessary to numb yourself against meaninglessness through diversions like alcohol or poetry) as unable to be a nihilist, because they are capable of distracting themselves from meaninglessness?
[0] https://poets.org/poem/be-drunk
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ETA: I don't think "is there anything meaningful in your life" uses the word "meaning" in the same was as the question "does life have meaning." Maybe the below commentor was totally correct about us all talking past each other, because the first question seems to ask "does anything reliably bring you joy" while the second asks "is there a purpose to existence." Someone could have things that matter to them while still thinking existence is purposeless.
What I hate is when people describe nihilism as "Well, I don't believe there is meaning but also I find satisfaction in the small things in life" or "There's no point in life, the point of life is to live". It's always the same pattern of rejecting objective meaning and thinking that's the same as having no meaning.
Fwiw, I'm in favor of Nietzsche's definition too, but I don't want to introduce a whole host of loaded words to an already confusing topic