So I've had the idea to make an interactive story by making a text adventure where the next part of the story is revealed when people guess what happens next. The idea is for them to do this by typing a word that is recognised as the "correct" answer, but I don't know if there's a way to make it so that they can type anything as long as it includes that specific word or phrase, and I want to give the option for readers to skip ahead to certain chapters by having a page of them where they can be accessed, but I don't know if that can be done in a text adventure or if that can only be done in a gamebook, which doens't have the typing option I'm after. Or does it? I'd just like to know what the best way to make my idea is.

I haven't used Quest that much, but there is a Scripts option where I'm sure you can make the typing portion of your idea.
As for skipping ahead via links, I'm not sure how you would do that in Quest.
You might want to consider using HTML and JavaScript.
Hope this helps! :)

Ok. Here goes my two cents. First lets talk about the technical issue and then we talk about the theory behind the idea.

Technically speaking, it seem pretty easy to implement. You will have the command prompt and then start the "guess the verb" process. Probably each "room" of your game will have only one recognizable command, what will be the one that follows your story. If you want a sort of "backup" option, you may have a general "password" for player typing like, "continue" that moves the player to a certain mainstream. I have been doing some experiments on making Game Books using the Text Adventure mode, by creating objects that are the choices. The idea is that the player scoops over the options presented as objects at the "Objects and Places" pane, clicks on "Look at" to know the details about that specific option and uses "Take" to pick that option. You could also do the same.

Now, about the theory of the thing... you sems to be planning a Game Book, but using what Parser has worse: the guessing verb game. Read a story and then pause it to try guessing what the player should type to see the next page may be hugely frustrating. People pause a Parser game for 30 minutes trying to make it advance because they are challenged by puzzles. Parser games are about being smart and solving puzzles. Game Books are about making hard choices to affect a story. Most of the Parser games don't have an actual story. They have a setting and a set of challenges inside this setting. If you want presenting a story, you need the three core story components: Setting + Character + Plot.

In short, what I am saying is that you should pause for a moment and check if this is really the kind of project you wuld like reseraching and implementing. If you find it is worthy a try, because you have questions about game design you want investigating, it wuld be ease implementing and you may count on me this whole wonderful community to help you developing your project.