What Half Life did well was its ability to immerse a player fully into a world and environment with the most barebones elements of plot. There is no extensive exposition, your character never speaks - you're literally dumped in medias res into the life of guy who, if it wasn't for the passing comments of some security guards, you wouldn't know the name of. And everything happens without anyone explaining it and somehow, it all works. You honestly do feel like you're living the life of Gordon Freeman - unlucky man caught in a terrible situation facing completely inexplicable things like aliens popping out of midair.
It's the opposite of most shooters nowadays - shooters now try to include as much exposition as possible to give you context and immersion, but in actuality, that can work against you - there can be too much contrast between the dialogue-heavy cutscenes with the best friend, the romantic interest, the commander, the main villain, the computer techie, etc. and the dialogue-empty gameplay parts where you just keep shooting moving things.
Half-Life didn't have that contrast and the developers did a great job setting the details to make sure the immersion was preserved. When a helicopter shot a rocket at you, no one told you, "Look out, they're shooting rockets. To dodge the rocket, take cover behind a wall, then shoot back!" or whatever.
However, on the flipside, it also limited the depth of story that could be explored. It never shifts to another perspective, there's never a long briefing. You're strictly limited to the perspective of one guy. So in Half Life, you don't get to meet a lot of characters, trace their arcs, their development, experience a richness of dialogue and plotlines, get all the backstory and necessary information for a deeper understanding of everything that's going on. Its strength of immersion also inhibits its storytelling - in fact, it doesn't have much "storytelling," really. It's entirely a slice-of-life - just a very traumatic and painful slice-of-life that happens to address the fate of humanity and the Earth.