Is it My Fault His Laptop Broke?

Possibly. You weren't paying attention to where you were walking and as a result, someone else's property was damaged. Whether or not you will be held liable is a different story.

 

Are you 18 years of age or younger than 18 years of age?

If you are a minor, your parents MIGHT be responsible for the damages.
Notice, I said MIGHT.
That legal determination has yet to be made.

If you are an adult, you alone MIGHT eventually bear legal responsibility for the damages.

Absent a court battle, no one has been declared responsible legally.

Moral responsibility, that's for YOU to decide.

 

On the other hand, if the owner ran the cord across a walkway where it shouldn't have been, you might not have had a duty to look down as you walked through and, therefore, you might not be liable.

At least you have a potential defense.

 

Also; IF the cord was where it shouldn't have been, it might help you to note that you could have fallen/tripped over the cord & been injured. (sounds like you actually weren't though)