This does not sound like a good-faith definition of terms. It's a no-true-scottsman instead, which is not a common practice, or at least not a reputable one.
Why bother with actual definitions when you can make up your own? This has been a common thread I've seen going around in my different groups lately. I don't know if it's the start of a new trend or a temporary resurgence of the fallacy. It's not like it's uninformed zealots either, many of the people I interact with are generally decent, logical people with serious flaws in logic. While I'm comfortable with cognitive dissonance, I'm not comfortable with blatantly twisting facts by people who should be aware that they are doing it.
i don't think the act of defining a term for later usage in an argument can be described as "no true scotsman", which is typically a mid-argument dismissal of a counterexample that contests a generalization.
to be such they would have had to (for example) been in the midst of debating the topic, and said something like "but a real abortion..." where their operating definition of "abortion" was effectively changed.
The term for this is a "stipulative definition." [1] It's only a fallacy if one does not clarify that one is using a stipulative definition instead of a more common one.