I don't know what specific problem Kelley and Meka were working on, but the connection between arithmetic progression free sets and computer science (especially communication complexity) is somewhat well established. See for example this paper[1] which gives new constructions of "corner-free sets" (which are closely related to 3 arithmetic progression-free sets) by thinking about a specific communication protocol.

[1] https://drops.dagstuhl.de/opus/volltexte/2021/14276/pdf/LIPI...