I'm not sure what your numbers would have to be to win the scholarship, but I don't think they'd be sending it to me with a 167 LSAT, if it typically goes to someone >175. There's no real justification for increasing the number of essays they have to review, other than that they want to take a look at a broader spectrum. At very least, it's an opportunity to pitch yourself as a candidate for scholarship money, and they might very well view this as an opportunity to take a closer look at people they're considering for money.
But, I would like to know if anyone has further insight into what the essay is supposed to be about. All I can glean from the package and the website is that you're supposed to write about something you've published, research you've conducted, or something you've invented. Is that it???
Also, I'm with you Amy... I got the packet and no acceptance.