Application looks too involved for Brown. When applying to 10 schools I wouldn't do this one because it has no overlap with my other application. I can reuse my letters of recommendation, I can't reuse this application.
I graduated quite some time ago. Getting letters of recommendation from professors would be impossible for me. I doubt I'd have one professor that knew me when I graduated let alone now years later. And yet, fulfilling these requirements would be very easy for me. I think it's very nice to have multiple routes in. Even if very few candidates avail themselves of this latter route, they might be interesting candidates worth strong consideration.
I'm in the same boat applying to a Master Program. It doesn't help that i spent the better part of my 20's as a business owner with no boss that can write a letter for me.
I think this would be useful for three groups of people:
(1) People who were planning to go into industry and already have, say, an offer letter from Google, or just a strong open source profile, but now aren't sure if they want to go into industry or academia. Being able to apply to Brown with their offer letter could reduce a lot of friction in their consideration of the academic route.
(2) People who've already tried to get into a top Ph.D. program the traditional route and failed. If this is your dream, and you don't have the grades or publications to get in otherwise, but you do have top programming chops, this could be a way for you to still get what you want.
(3) People who are already in industry and want to go into academia. They may have lost their academic connections at this point in time. Even if they had great grades, they may struggle to reconnect with old teachers to write the requisite stellar recommendation letters.