I don't think we really need clearly defined, heavily scripted quests like "Our planet is being attack by Zargons! Will you save us, space hero?"
In fact, perhaps they shouldn't have dialogue at all. Minecraft provides a good example of how quests could work. For example, in the game you can choose to find a portal to another dimension and battle a powerful dragon there. Nobody tells you to go battle the dragon. You don't get anything useful by killing it, other than bragging rights. It's just a fun challenge you can choose to do because you want to.
So "quests" in Trillek could also be dialogue-free things you choose to do, just because you want to. For example, maybe there's a huge alien space station floating in orbit around a planet. Every time you get near it unleashes a powerful barrage of lasers at you. You can choose to leave it alone. Or you can go fight it. Maybe you'll get some cool loot or tech by destroying it, but it's not something you have to do. You could just leave it there and steer clear. But players won't do that. They'll want to take on any challenge the game throws at them. There's no need to tell them to blow up the space station. Just put it there and players will provide their own motivation, and will design whatever ship they need to defeat it.
I think a lot of the writing can just be thinking up interesting scenarios like that, without having to explain exactly why they're happening.