An example I have personal (and extensive) experience with is Morrowind's Gamebryo, which is exactly the same base engine that was used for Oblivion, Fallout 3, Fallout New Vegas, Skyrim, Fallout 4, and Fallout 76. Frame timing for all game functions operated off of 60 FPS or less. If I increase the FPS beyond that point, things like player movement speed, idle animations, weapon attack speed, etc. will be accelerated linearly with every frame over 60. The functions will be based on the number of frames that are actually drawn to the screen.
Physics calculations were taken based on keyed frames that were rendered and drawn to the screen, again ticking complete cycles every 60 frames maximum. If the FPS exceeded 60, or if multiple, partial key frames were drawn (because of unlimited FPS / vsync off), the additional frames data would be treated as a multiplier to the physics calculations, and would result in a "physics explosion". (I bump into a cart, and it flips over sending a cabbage into orbit.)
But most shockingly to people struggling with "unexplainable" glitches and errors was the fact that Papyrus scripts (which is Bethesda's scripting engine that manages everything concerning quests, weather, day/night cycles, random NPC population and placement, animation packages, Radient AI behaviors, etc. -- everything that makes the game "do stuff")...also operates on a timer that uses 60 FPS frame timing to function. Frames passing is what counts as "ticks" on its internal clock. If I exceed 60, it means that the clock is now running in fast-forward. All sorts of broken stuff can start appearing.
Other games that use similar frame-timing functions that I know of: Dark Souls 1-2, Dragon's Dogma, Drago Age: Origins through Inquisition, Mass Effect 1-3, Halo 1-3, Supreme Commander and Forged Alliance, Total War 1 - Medival 2...each of them suffers from some pretty serious issues if FPS exceeds 60 or 72 in various cases. It's not always a guaranteed issue, nor does it mean that player are aware that issues are occurring. But they're there.
