They were not even remotely seen as horror exclusive but around 2008-2010 those elements became exclusive to horror games. Actually something very similar happened with most genres after 2005.
The end result is that you now have two generations of gamers who use the same terms for wholly different things. So when a 90s guy like the one the in video talks about action adventure he is talking about a style of game that a zoomer would describe as survival horror.
This is an interesting observation, because I'm not a fan of horror games at all. I don't care about them, just not my genre. But I love oldschool action adventures with high tension.
I think the main problem is that game design principles have changed so far that most classic genres have become inconceivable to modern designers.
Back in the day, Tomb Raider's design was very close to what other games were doing: it plays a lot like a 3D version of Prince of Persia. FPS games like Quake, released in the same year, had a similar atmosphere when it comes to level architecture and mood. This was just the way games were designed.
From the mid-00s onward, game design principles had shifted away entirely from oldschool game design. Tension and pressure were removed in favor of handholding and a guided experience. Games no longer allowed you to be alone with yourself, trying to figure things out. Instead, they led you through a cinematic experience where failure was not an acceptable consequence for bad play, but something to be avoided.
The focus on puzzles and tough platforming that requires you to figure out how to get to places also reminds of classic text and point & click adventures. Those also had long moments of letting the player analyze problems and figure them out, without handholding or other forms of intrusion.
Action adventures were genuinely
adventure games, inspired by the genre of the same name. But most young people have no connection to the adventure genre anymore.