Just from memory.
Far East of Eden Zero on the SNES had a battery powered real-time clock to keep track of real world times and dates and schedule things around them.
Black & White 1 had an online connection that was pretty fascinating, I pirated the game(0-Day!) and played it a couple of days before release and a developer through a villager questioned me about it, I had pre-ordered the game and was hyped so I pulled it early, he was satisfied with that answer. This is extremely forgotten by people because there can't have been many that experienced it. It also had a thing that might not have worked where the main server gather weather information and if it rained where you lived it would rain in the game.
Boktai. Vampires hate sunlight and the cart had a thing that could tell the difference between normal light and sunlight(probably UV or something).
Ingress was a cool idea, made by Niantic, the Pokemon Go people. It was a real world game so time was of course based on real time.