Um, well, actually, a rocket fired at an angle can still reach escape velocity and leave the earth. It becomes a question of power; or, the duration of the application of power.
A rocket fired at a 45-degree angle to spinward of the planet gains some small momentum from the rotational energy of the planet. A rocket launched at an angle will follow a parabola, as it's influenced by the gravitational acceleration of the planet below. If the amount of energy applied is insufficient, the parabola intersects the earth, and of course the object will impact elsewhere. Think ICBM. But if acceleration is simply maintained to escape velocity, the parabola doesn't intersect the earth, and the object will escape into space exactly as if it had been fired directly outward.
The truth is, we fire rockets straight upwards now because it is the cheapest, most direct way to orbit or escape. It minimizes the time in atmosphere, which equates as drag, and only requires a short amount of time under a high expenditure of energy to attain, which is the way our propulsive technology operates today.
With a technology where power is simply abundant, a much more leisurely approach to space is is entirely possible. Propulsive technologies of the future may be radically different from what we know today in their ability to deliver power over a sustained period of time.
I only say this, as it may or may not impact on the future of the story (no spoilers!).