It can be hard to define bad writing because there's a wide range of reasons for why a game can be written poorly. Flat characters, cringeworthy dialogue, nonsensical plots, uninvolving narrative plot structure, painful prose, etc. etc. Sometimes there's too little writing, and then sometimes there's way, way too much. Shit, sometimes even the delivery can make otherwise decent writing seem awful.
In general, people say video games have poor writing because, well, they do, for the most part. For a while, plots were either nonexistent or extremely brief justifications for the action on screen ("The President's been kidnapped by ninjas! Are you bad enough dudes to save him?"). When developers tried to add stories to their games... well, developers aren't writers, and it showed. Even when professional writers were brought on board, many wrote games as if they were writing movies or television programs. We still get this; how many games have stories that seem utterly divorced from the gameplay?
Video game narratives remain stunted because there's no demand for great writing, for two reasons. First, many people just don't care, which is fine. Some games really don't need flowing narratives; sometimes, you just want to jump in and play. The second, and more damaging, cause is that people will rally around and praise awful writing. Take Bioshock Infinite, a confused mess of a story revolving around quantum mechanics written by a man
who admits he doesn't understand quantum mechanics. In any other medium, the script would be laughed out of the room, and yet put it in game form and it's compared to Citizen Kane. This lowering of standards encourages and enables poor writing, and does nothing for the industry's reputation.
Another example is Bioware. They're a studio that's been lauded by many for having some of the best writers in the industry... and
this is the writing they're turning out (none of that text has been altered). Imagine looking in from the outside and hearing that this is supposed to be some of the best video games have to offer; it's going to give you a pretty poor impression.
So this sort of became a rambling rant, but... video games' writing problems are far, far deeper than perception. People say video games have bad writing because a lot of video games do have bad writing. Some video games have good or great writing, too. If we want to change the perception of writing in video games, we need to promote these games and demand more from game narratives in general. We shouldn't lower our standards; we need to raise them. If developers are going to bother with a story, we should demand good stories, or, hell, just functional ones.