It may not have been for sport. Foxes, I've heard, stock pile for later. So, they may kill 3 chickens and only eat one... they hide the other 2 and come back later. I've never had this happen, but my neighbor did a few years ago. 4 birds gone. No sign of 2, but he found the other 2 in the woods partially buried. He set a trap and caught a baby fox. He let him go.
Maybe that's not the case here, but that's what I've heard.
Sorry for your losses, in any event. We've been battling a fox (probably the off spring to the above!)- we had been free ranging and he killed 3 in one day. We've penned everyone in a brand new run- we've seen foxy pants pacing the run TWICE. We hope he gets the hint after the last attempt. DH managed to get him good with the hose, of all things. Dogs took after him into the woods.