If there’s anything that’s meaningfully different from other schools, I’m not aware of it. If you were a first-year applicant, my answer would be “an Early Decision application,” since WashU likes students for whom they are a true first choice (not an Ivy back-up) and fills a large share of their entering class with ED applicants. But they don’t offer an ED option for transfers, and they don’t track demonstrated interest either. So I think the best answer is that they’re looking for a compelling answer to the “Why us?” question that wouldn’t apply equally to every other school on your list… and they want to see something interesting and distinctive about you that will add to their community. But of course both of those things are true of other schools too.
That said, I don’t have much personal experience with WashU, so it’s possible that others will have more insight to contribute.