I think that was the cat's way of showing loyalty to you by providing you with fresh caught kill. It was in that way acknowledging that you were the alpha.
Both my kitties were indoor kitties, However, I put out a bird feeder for them. They would watch from the safety of an inside window of course, fascinated with the birds while I was at work. I'd see them on weekends. Their eyes would stare, they would salivate, their paws would flex, and I would wonder what these little guys were thinking. Do birds taste like chicken?
You can take a domesticated kitty out of the jungle, but in the end, she's really not 100% domesticated even though I gave them so much food, toys, and warm places to sleep they didn't need to chase anything other than the red dot.
Oh well. Still love them. Still proud to be a cat lady.