Here's my opinion of the workout;
Firstly, you're not using your back for power. Punching is always about torguing the body. This means you're not twisting those hips, that upper body and most of all your feets are planted like a tree in the ground.
Mostly arm punches...
Secondly, you keep dropping your hands every now and then. I see what you were doing there... To fake a punch, you need to telegraph it! Bend those knees, lean forward with the lead hand, extend the arm but bend the elbows so your hand goes down.
A good fake is one that let's you economically set you up for another strike i.e. fake a lead to a cross.
Thirdly, keep hands up?
Fourthly, You're not stepping in with the punches. You're just not generating enough power by standing still. When you jab, you need to step in. When you punch, you step in. Period.
Fifth and last, if you're going to punch to the lower upper body, you need to drop level to punch. Only punch at eye level. If you're going to punch the chest, you're going to need to bend your knees so you drop a level down, then push with the rear leg and deliver the punch.
Get the instruction from a qualified instructor before proceeding. You may just injure your hands if you keep doing this.
Who said boxing's easy?
I got two fists.. Don't make me use my head as well!