I think they want to show how she started off. Notice that by the end of the video, Lara was pretty much her bad-ass self. I think they want to give her human, specifically feminine traits because the end-product of the original felt more like a guy with breasts, if like a human at all. They want her to be more realistic and to establish a connection with the player on levels other than "boobs".
That, and Other M's problems are often blown out of proportion.
Well by the end of the trailer I was watching her still scream and cry and almost get raped or something. I mean yeah you saw her climbing and running away from airplane blades and she'll have more character than the original Lara Croft but I don't want her screaming and bitching so much. It seemed more like her crying and going "I CAN'T DO THIS DADDY ISSUES" instead of her going "Well, I'm in a shit situation, but toughen up buttercup and kick some ass!"
With female characters that are previously seen as "independent" and "strong", it's risky business to make a prequel that shows how they got there. Admittedly Metroid Other M wasn't a prequel to the whole series (which was one of its issues) but it's hard to make the character develop to be strong without them coming off as too much of weak cry baby in the beginning.