Learn English – Meaning of “dress style”

Dude — you're cramping my style!

means that "Dude" is behaving in such a way as to inhibit whatever behavior the speaker is engaging in at the moment — whether that be trying to have a conversation, playing a game, trying to get romantic with a woman, whatever. Say I was in a bar chatting up some hottie and you walked over and started trying to sell me insurance, I might tell you you were cramping my style.

The idea of using train-wreck to describe a person comes from not only the awful calamity of a literal train wreck, but also the macabre pleasure that the general public seems to derive from viewing such a spectacle. It is the morbid interest that we have in watching other people destroy their own lives that really gives "train-wreck" its meaning.

"Train-wreck style" is an extension of this idea. In your example, Anne Hathaway's character "offers an indelible, if sometimes repellent portrait of a recovering addict who makes people squirm." Her character is the train-wreck; the speech she gives at her sister's wedding is delivered in a "train-wreck style" because we can all see the awkward and embarrassing end of her disastrous attempts to heal from her addiction, but we can't help but watch her anyway.

EDIT:

You asked whether "self-destructive style" could be substituted for "train-wreck style" and it is similar, except that "train-wreck style" is publicly self-destructive. You cannot be a train-wreck in private, although you might be very self-destructive in private.