This is a good argument, it's certainly less depressing than the idea that games aspire to being bad John Carpenter movies.
I would argue that "written" is the wrong term. Storytelling in games is more than just the writing, as per film.
In terms of storytelling, we have some amazing examples, such as Journey. The gameplay limitations and art are focused to support the direction, and results in an emotion from the player that is unique within the medium. The Last of Us uses cinematic techniques (character performances, direction, camera angles) along with the written script to do the same. GTAs are written brilliantly, for the most part. WoW too, if you take the time to read and experience the story - though its hard when you have so many pelts to harvest.
Even badly written games can be successful in their narration, providing the pieces all fall into place, and vice versa.
Some simple plots just fit well around their game concepts. Atari's original APB had just the right amusing interludes to fit the gameplay, like the doughnut-eating cops and being chewed out by the lieutenant at the end of a mission.
On a higher level, the interleaved scenes at the start of Fahrenheit by Quantic Dream where you are simultaneous covering your tracks and investigating the murder at the diner work very well.
I found Bioshock Infinite very overwrought, the plot and game were too divergent - I guess that's what happens when the makers over-focus on the story.
Characterisation is a tougher part of storytelling in games; most people seem to prefer sidekicks like Alyx in Half Life 2, but their constant presence means that scripting becomes very obvious. I found the NPCSs in Dishonored well sketched out for the small amount of time they appear. I was even a bit taken aback when the boatman turned around and said he was disappointed in me. The bad guys seemed sufficiently motivated and venal to be actually evil. The good guys are bad, it's all pleasantly complicated. The key is to draw a character in a situation and then make them disappear before they start to repeat themselves.