Why Do You Punch Like That? 

Makes sense. More vids like this please!

I mix straight punches with backfists from a standing position. I move just the same as a hook but move to position my opponent directly towards a fastball, ie the backfist from the right. Then follow that with straight punches or backfists depending on distance and momentum. Backfists also easily setup clinches. A tip I learned from a muay thai friend, from the clench, place your head hard against your opponents and use your arm strength plus your neck and upper torso to force your opponents head and body to where you are bringing your knee, as opposed to aiming for them you line up ths strike. I have never seen it done lol. Just drilled it. Try using your head from the clinch, it's easy to direct a person even stronger than you, where you want them. If you are quick you will cause them to lose balance and easily strike or take them down in combination.

Didn’t Carl cestari show this when showing bare knuckle boxing as well ?

It's to recover in preparation for the counter.

how about the uppercut?

Do you turn your fist upon impact? Should you, even?