That's what I meant by saying she essentially says she went to her local CVS by specifying the city and state of where she lives, and that she went to her local CVS. Maybe she didn't need to do that, but it is a leap to state she did it for malicious reasons. More likely it was to provide some context.
I don't know how she feels about the pharmacist getting fired. It is possible she does feel bad, and that she didn't want him to get fired as much as she wanted him to have a better understanding of the pharmacy needs of transgender people. It is possible she feels good about this pharmacist no longer being in a position to harm other people because he was fired, but it is also possible she would have preferred that he apologize, developed a better understanding of her needs, and still kept his job. Your guess is as good as mine. But the blog post really doesn't read as vindictive to me as it does to you. She never says she did this to get the pharmacist fired. She also never mentions the pharmacist's name or the specific store where this happened, which to me indicates this isn't about some personal vendetta.
CVS probably decided to fire the pharmacist because he violated company policy, state law (by refusing to transfer and refusing to give back the prescription to the patient), and potentially federal HIPAA and anti-discrimination laws. There was practically no way for her to get her story out (without it being overly vague and unhelpful) and not putting this pharmacist at risk of getting fired. So whether her motivation was revenge or justice, I don't really see a way she could have gone about telling her story that did not end up in the pharmacist getting fired. Even if she said explicitly she didn't want him to get fired (maybe she really just wanted an apology and the pharmacist to go through some training, and maybe he refused), CVS probably would have fired him if it turned out what he did was true.
I agree people shouldn't mess with other's livelihoods unless it is warranted. We don't know enough about the material facts to make that judgement. If we just take what the patient said at face value, CVS has plenty of good reasons to fire the pharmacist.