The most important factor in determining the ease at which a game hits 60 FPS, is definitely the engine. You can have the fastest CPU out there, but if the engine is crap, then getting to a
steady 60 FPS will be damn near impossible. Then I think the API is secondary, and hardware comes last.
Some engines are just amazing in how well optimized they are for hardware. The latest and greatest example of this is Id Tech 6.5, which uses Vulkan exclusively. That engine is flat out incredible in how efficiently it utilizes the hardware, and how well it scales on multithreaded CPUs. With my 6900K, it's very rare that I drop below 100 FPS in the game never mind 60 FPS, even with tons of stuff happening.
And the amount of sophisticated graphical effects and the frequency at which they are used is also very impressive. For an example, the game's volumetric smoke and fog effects
universally accept light and shadow from the environment. Usually this kind of effect is used very sparingly in games, because it is computationally expensive. Doom used it in fact, but not gameplay scenarios. Wolfenstein 2 on the other hand uses it very often, both in the environment and in gameplay scenarios such as the one below, which I took from the Digital Foundry video.
As you can see, the smoke from the explosion is being affected by the fire and the particles which are lit.