As a condensed matter physicist (working in the same field but not on altermagnetism specifically), I would say this is being much more picky about the language than most people in the field tend to be. Moreover, I'm not sure you're even right about the language.

You are correct that this doesn't involve any changes to our understanding of electromagnetism in general; whether or not that means that altermagnetism is not a new type of magnetism is a matter of semantics. If I read in a paper or heard in a seminar that "altermagnetism is a new type of magnetism", I would not quibble with the language, though that phrase by itsself is almost tautologically pointless.

If you want a more technically meaningful phrase, I would propose that altermagnetism is a newly-discoved "magnetically ordered phase". Of course that doesn't fit so well in a headline.