[JulianWasTaken]

That's not the operation from the question in the link (not that I'd be terribly surprised if Sublime Text had a way to do it anyways, but it's not as fluid as vim).

[Shorel]

My bad.

To fix my blunder:

Delete rest of the current word (and go to insert mode when applicable)

Vim: ce -> ST2: Ctrl+Delete

Delete current word (and go to insert mode when applicable)

Vim: caw -> ST2: Ctrl+D, Delete