I wonder how successful attempts to replicate it have been. Couldn't find anything on that either.
http://www.ajhepworth.yolasite.com/resources/9822-a2.pdf ha a writeup on page 277 and cites:
Ward, G., & Keltner, D. (1998). Power and the consumption of resources. Unpublished manuscript.
PDF: http://www.communicationcache.com/uploads/1/0/8/8/10887248/p...
https://web.archive.org/web/20101205211147/http://socrates.b...
And an article:
https://greatergood.berkeley.edu/article/item/power_paradox
I'm reading "The Undoing Project by Lewis at the moment, finding it slow going, but interesting.
From that, here's the actual paper. Little methodology description, no significance testing, no indication of the number of participants or how they were selected. This has significantly diminished my belief in the proposition that power makes people more selfish in the cookie scenario. I still believe it is somewhat more likely to be true because of my priors, but this study didn't contribute much.
I included the paper, the precise link, in my OP.