The subject of "Martial Arts" is not just limited to unarmed techniques or Eastern styles, but applies to ALL combat forms. And there're ALL called "Martial Arts", since acronyms like "HEMA" (Historical European MARTIAL ARTS). "Martial Arts" is not even an eastern language term.
Isn't that the point of the complaint? I agree with your point here - but that problem is that in practice, almost no one refers to Conan the Barbarian as a "martial arts film" or Errol Flynn as a "martial arts star". For example, in my copy of GURPS Martial Arts (3rd ed), the cover has a yin-yang symbol and there are seven weapon tables: Chinese, Japanese, Ninja, Philippine, Indonesian, Indian, and Korean. So clearly it's not about all combat forms but rather focused on Asian forms.
Unfortunately that's true, and it came about after the term "Martial Arts" became associated with eastern unarmed styles with the influx of Martial Arts films in the 70s, which continued in the 80s and somewhat the 90s.
However, that was at the turn of the last century. We're living in 2020 now. HEMA is all over YouTube. People know about Capoeira, Krav Maga and other non-Eastern martial arts as well. People should know "Martial Arts" extends beyond just eastern styles of unarmed combat by now, and even if they don't they're still in error and need to be corrected, not change the meaning of the term "Martial Arts" cuz some people are idiots.
This was a pet peeve of mine even in the 90s (the decade I started playing), and I would frequently correct people when it came up during play or character creation, and point out that swinging a sword itself was a martial art.