
The first modern karaoke was on the Atari computer. My bit of knowledge on the subject.
I would like to preface this by saying the bouncing ball sing a longs came first, but I don't consider that to be modern karaoke where you pick a song to sing to. These were usually group sings in a theater, and later television.
Reading lyrics off a sheet with a cassette doesn't really capture what modern karaoke is, which is lyrics sweep/highlights to the music.
The linked video was from a video game released in 1985 called Alternate Reality, the City. The music system used for it was custom created for the game, and later cloned into the Antic Music Processor in 1989.
For a time BBS's had almost every song you could think of transcribed into this system. Even Billy Joels Scenes from an Italian Restaurant, or Aerosmith's Dream On.
Modern because, you could connect to a BBS online, download a song in an extremely small, efficient format. This predates pretty much everything modern, like midi karaoke.
While we can compare CDG (which was 85) and Laserdisc karaoke (78) Neither was in a conceivably small, downloadable file format at the time like karaoke is now.