I think i'd normally leave my head in the centreline but defensively i'd move more than they have shownin this video. I'll just leave that as my opinion though and let a coach give you a more informative answer.

I do however have more Qs based on your little vid open to anyone who wants to answer.

1) Since when was the word cross considered slang as opposed to straight right?

2) I think this is boxing for kickboxing so unlikely to be geared to the same type of movement. Plus i know they need to keep the drills simple.

Still doesn't it seem odd that the defence even just for the jab alone doesn't involve a step in any direction?

When it comes to even just a jap with any kind of weight behind it i would always be left off balance trying to parry it without a step.

3) Isn't it potentially dangerous to over rotate your fist past horizontal on impact?

I would have just though allowing the thumb to drop too far down would be leaving your wrist and maybe elbow and shoulder in a vulnerable position?