For example, when i move it to the right, it is supposed to stay put right? It doesn't stay, it returns to the middle again, to its original position. Pretty much, the accuracy is the problem here.
No. Your supposition is incorrect. The accelerometer reports instantaneous acceleration values (change of velocity/speed). If the accelerometer stops moving, the velocity drops to 0. So, eventually, you see no change in velocity.
A video that shows some Arduino code that is completely unrelated to reading accelerometer data is worse than useless. It wasted 3 minutes of my time.