They have trained chickens to discern between male and female faces. It would be logical to assume that they have found features that allow them to put each sample on that one-dimensional scale, and then use those features. It would mean that a more "beautiful" face is the one that is most distinguished in it's features from the face of another sex.
This would be the most naive interpretation, but as always in nature, there can of course be layers of complexity on top of this.
Another, related explanation might be Occam’s razor (the preference for simple things [3]): Beautiful things are beautiful because they are simple. They require fewer bits to be represented and brains prefer such representations. This is a fact that possibly also explains intrinsic motivation and our interest in art and science [4].
Another explanation might be that chickens have evolved abilities to recognize symmetric body shapes and a uniform skin texture for their own intraspecies visual (sexual) attraction. Sexual attraction to symmetry likely mainly exists because asymmetry is reliable evidence that growth hormone signaling was not only out of tune in some regions of the body (e.g. the face), but throughout the entire system and this is the root cause of all kinds of diseases (e.g. faster wearing joints) [5].
[0] https://en.wikipedia.org/wiki/Poser
[1] https://www.facebook.com/nipsfoundation/videos/1555427447881...
[2] https://i.imgur.com/Xs4njxa.jpg
[3] https://en.wikipedia.org/wiki/Occam%27s_razor
[4] http://people.idsia.ch/~juergen/creativity.html
[5] http://www.aiai.ed.ac.uk/project/oplan/documents/1999/1999-M... (Entry "Section Sexual Attraction, Evolutionary Psychology of", p. 884. The entire entry is well worth reading.)
Anecdotally however my father used to have one that not only recognized us (all people in the family) from a distance, she would also act as a guard dog if anyone else entered the court she lived in.
OT, and probably re-known, however here is the story of Mike, the headless chicken:
Citation: Ghirlanda, S., Jansson, L. & Enquist, M. Hum Nat (2002) 13: 383.
Link: https://doi.org/10.1007/s12110-002-1021-6
DOI: 10.1007/s12110-002-1021-6
Abstract: We trained chickens to react to an average human female face but not to an average male face (or vice versa). In a subsequent test, the animals showed preferences for faces consistent with human sexual preferences (obtained from university students). This suggests that human preferences arise from general properties of nervous systems, rather than from face-specific adaptations. We discuss this result in the light of current debate on the meaning of sexual signals and suggest further tests of existing hypotheses about the origin of sexual preferences.