The statement to me is patently ridiculous, but it makes sense if you look at games in a certain way. The singleplayer gameplay in a modern shooter serves what end? You walk through rooms of dudes and shoot them. Why not just make a movie about that? That's one of my hangups with Spec Ops: The Line, if you've ever played that game or heard about it. That game is a statement about modern shooters, so in that respect it's good that it is a shooter. However, basically the entire game would have been better if it was a movie. The combat in that game serves no point except as a backdrop to tell the story.
That's a big problem with modern games. We create gameplay that isn't novel anymore and don't use it to serve any purpose except tell a story. We make games that are designed for the player to win, but don't do so in a way that is interesting or fun. I'm really looking at shooters here because they're the worst offenders, but the same can be true of any other genre. Let me state some pretty big blasphemy here: the best Final Fantasy games would be better if they were books or TV shows. Very few Final Fantasy games do anything fun with the gameplay; it's just a means to get to the end. Final Fantasy VI is the worst offender; you barely have to even try to beat the game. It's just that easy. Final Fantasy VIII is even worse since the gameplay actively hampers enjoyment of the game.
Good games create an experience with their gameplay, and sometimes that's hard to describe with words. Metal Gear Solid (the original on PSX, not the remake on newer consoles) did a really good job of putting you in the shoes of this super-spec ops guy and showing you the dangers he was going through. Rooms were puzzles, but you could solve them in your own way; violently, stealthily and virtually any inbetweens. The game even gave feedback on how well you did. The gameplay was a huge part of the experience of that game, and if you played it for the first time, you felt really smart when you figured out the latest trick or puzzle. Skipping the combat (or perhaps action is a better word) in MGS is like skipping an entire movie except for the credits.
As designers we shouldn't just say, "I just want to create this story, so I'll make a game around it." The entire point of video games is the game part. If the only games you were exposed to were Dragon Age and Mass Effect, I can understand skipping the action parts because honestly other games do those things better; all BioWare games are about telling your story. They're basically visual novels that have gameplay added on (notable exception being SWTOR which has evolved quite a bit into a "real MMO").
In case weren't aware, I'm pretty hard on shooters. There are a lot of shooters that have been released that push the envelope (HAWKEN, Loadout, and especially Strike Vector) but the majority of shooters are really just old rehashes of the same boring shooter formula. Most action RPGs are too, honestly, but I'm less harsh on them because the people playing them really like that sort of gameplay (I play Borderlands 2 still, so I'm not exempt). I feel like shooter and to a lesser extent JRPG gameplay has become really stale. I do like that more games are branching out with stuff like DayZ, but then there's games like BioShock Infinite that are basically nothing new. Yes, I understand you're telling a story and showing a world, but why not do that in film? Depressing from the franchise that brought us System Shock 2.
The point of this rambling is that more developers should actually do something with their gameplay that makes their game worth calling a game. Even Long Live the Queen did it for visual novels (it's really good!) so I really think it shouldn't be that hard to create something that gives a new experience for a player without just telling a different story.
PS: Story's not a pillar of games and it never will be.