I do wonder if there are patents on this, and if that has prevented other devices from adopting this kind of protocol?
WiFi has always had AdHoc mode which enables two devices to directly communicate like they were on the same Ethernet link, and I've used it a few times for a similar use-case to yours. It seems AirDrop is just a layer on top of that which facilitates the configuration required, but otherwise it would probably not be too difficult to "roll your own" similar app.