Actually, one of the articles on the subject mentioned that the SeatDefender device that was used was not allowed, which would imply that the property rights are at least implicitly assigned to the recliner.I have not seen that. But if true then the airline just has to make clear what the property right is and let bargaining take place or while the SeatDefender may be illegal it still doesn't necessarily mean that property rights have been defined. Use of the device may just be an attempt at "homesteading" legroom.
Update: Economists Do It With Models has kindly provided the source that mentions the device being banned: http://consumerist.com/2014/08/26/united-flight-diverted-after-passenger-uses-banned-seat-recline-jammer-starts-scuffle/
Also from the Environmental and Urban Economics blog comes an Update:
Yes, I am well aware that the Coase Theorem assumes that property rights are well defined and agreed upon (so some have said that the Coase theorem does not apply here) but what is interesting about this case is that the airline has not established these rules. It is also interesting that transaction costs precluded the ability of others on the plane to offer their seat to the woman who wanted to recline because this simple solution would have resolved this "crisis". Nobody gained by landing the plane in Chicago. People lost time, they had to land and takeoff one more time. The Coase theorem assumes a smooth redistribution of resources but instead resources were destroyed in this multi-player interaction. This should interest economists.