The paper is basically like this (spoiler alert):

“Some random user on Reddit posted a picture claiming that this is the longest straight line path on water possible on the Earth. We implemented a smart algorithm to solve this problem, found the elevation data, ran our algorithm... yes, that random user was right. Also, here's the longest path on land.”

Thanks, I really enjoyed reading it, even though I hoped that they would disprove the original claim!

Edit: here are the gcmap links to the two paths: sea [1], land [2].

[1]: http://www.gcmap.com/mapui?P=25%B017%27N+66%B040%27E-58%B037...

[2]: http://www.gcmap.com/mapui?P=24%B033%27N+118%B038%27E-37%B02...