The sollution to your problem is very easy. Click and hold the upper blue bar and drag the entire window a little bit down and to the left. Now you can hover over the rightabove corner of the screen. There will appear an arrow in a 45degree angle. Click and hold an drag to the lower left to change the size of the window to whatever size you want it to be.
Now close Media Player and restart it. You will see that it's the same, smaller, size that is was when closing.