I didn’t work on Lightsail, but the article implies that it does aim the sail. It isn’t expanding/contracting, but it does change orientation using the reaction wheels. Basically, they turn the sail broadside to catch the sunlight to raise the orbit, and turn it on edge when they don’t want the extra drag.
This particular satellite won’t ever leave orbit because the sail can’t overcome even the tiny amount of atmospheric drag. If you want to achieve escape velocity with a sail you’ll need a bigger sail and a higher orbit to start out. Right now it’s only feasible for small satellites and we’ve been able to achieve escape velocity using rockets for decades.
Eventually, I do envision a competition to see who can get a payload to Mars with the least amount of fuel. Kind of like the fuel efficiency challenges that college engineering departments participate in today.