It's not actually a "railroad" when you get to play it. Instead, think of the "GM turn" / "Player turn" just as being who gets to frame the scenes.
First off, the PCs are Guard Mice so have a mission. Then, the GM gets to frame two (and only two) obstacles to achieving that mission, and those are resolved by one of success, success with a Condition, or a Twist. Once the GM has framed those two obstacles, they're done. They can't frame any more scenes until the players have had their turns.
Then the players get to take control and say what they want to do. The PCs have the Goals to pursue and the Beliefs to test and challenge (and the players wrote them, so they're invested in them.) The players pick objectives and frame scenes around them, and the GM has no choice but to react to them. That happens at least once per player, or more if the players earned Checks in the GM turn.
Only once all the player turns have resolved does the GM get back any control of the direction of the game.
Compare that to a more traditional structure, where the GM is in control of all the scenes, and the players can only react to the scenes the GM is framing.