No, this just isn't what the word means, either popularly or in technical usage. I can't find any dictionary that restricts karaoke to covers, and if anything the dictionary emphasizes non-covers:
> an act of singing along to a music video, especially one from which the original vocals have been electronically eliminated.
https://www.dictionary.com/browse/karaoke?r=75&src=ref&ch=di...
It's true that in practice most karaoke audio tracks are covers for financial reasons, but that doesn't change what the word means. Most tables have four legs, but six-legged tables are still tables.
I agree that it's not what the word inherently means, but it's the typical situation (which is effectively like meaning) where I am (USA).
See the many examples (in the West) of tools that remove vocals from audio tracks; they are ubiquitously described as useful for creating karaoke audio tracks:
https://tunebat.com/Vocal-Remover
To me karaoke is just signing to music, which is exactly what this is. I found it very strange that they avoided that word.
Properly licensed karaoke tracks are covers, because licensing custom remixes of original tracks is prohibitive. There are sites where you can buy stems/backing tracks of any song you can think of, which are reproductions by talented musicians.
https://www.karaoke-version.com/custombackingtrack/wham/last...
Regardless of whether you believe it's an "essential property", that karaoke music often sounds cheesy is one of several reasons Apple wouldn't want Apple Music Sing to be associated with it.
Apple's footnote disclaimer says "does not fully remove vocals" and "kara" means "empty/void" so it kind of makes sense to avoid using such an absolute term to describe something that isn't.
that's more the definition of "cover" than "karaoke" (which is a live sing-along at a bar or at home)
The real surprise is that the artists are ok with this, they must be getting compensated.
This Apple feature seems to be where the same popular recording gets used, which has vocals, and then some magic processing reduces the vocals.
There has always been software to sorta-kinda suppress vocals from existing recordings, but it usually ends up sounding like trash (artifacts of all sorts) compared to just having a karaoke band re-perform the song (although the talent and production quality can be dubious with the latter). Presumably the innovation here is not having vocal suppression sound so bad.
Aside: and then there are popular artists who release an instrumental version, or stems from which an instrumental version can be trivially created, but this is so extremely rare as to not even be on-topic for a conversation about broad availability.