Games, by their very nature, didn't start out having a story. The very first game was a sort of Missile Commander, which became a sort of Tennis, which lead to Pong. Games didn't need much beyond 'here's the situation, GO!' even when they moved to arcade games, which you'll find is still the case for most of them.
Games for the home consoles/PCs have evolved over time, however. As they became more advanced, developers started to create better stories. Your lead characters had histories beyond 'killing machine', there were plots that could change over time, dialogue was placed throughout the games, and so on. As gamers grew up, so did their games.
When games went 3D, people really started to become immersed in them. Before, everything was on one plane and it was hard to relate to characters like that. But now you could go anywhere! Do anything! It was brilliant! It made telling a story much easier too, by having characters actually move and talk in a manner like they would in real life (to a degree).
Cutscenes were no longer static scenes, things could happen all around you. The camera could sweep in and out, things could blow up, characters could react to events in real time, etc. It would really draw people in and was a huge hep in getting across the plots, which had also become more advanced to meet these new techniques of storytelling.
These days, things haven't evolved much since then. Sure, graphics have gotten prettier, but storytelling hasn't really involved much since those early days of breaking through into 3D. Yes, we have great looking cutscenes and fun gameplay, but where's the story? Are we being told anything while we're playing, or are we simply stumbling around from one objective to the next?
Some games break the mould - Half-Life had a good story, but nobody actually told you what it was in one big info-dump so most people can't really remember it. Deus Ex and System Shock 2 both had fantastic plots, but you had to dig around to get the full thing, and a lot of people couldn't be bothered after a while. Adventure games are literally structured around story, but they fell out of favour with the general populace and have only recently started to come back, and even then it's mostly as comical affairs.
Until people realise that games need to integrate with stories to advance the medium, they're not going to advance at all, and we'll end up stuck in a rut. I hope developers get that and try to break out of it - even if they don't fully succeed, some of us will still recognise and appreciate their attempts.
