The SNES is a 60fps system. This gif is just really sped up for some reason.

The system did not have enough memory for a frame buffer. Because of the demands this placed on the video hardware, frames always takes the same amount of time to render (regardless of their complexity - a black screen took the same render time as a bullet-filled space battle), and data could only be uploaded "between" frames, during vertical blank. The hardware is designed to make this easy, sending an interrupt once every frame at the start of vertical blank.

Almost all games have their main loops synchronized to that interrupt, and therefore run at 60fps. It was actually harder to make a game that ran at less than 60fps than to make one that did - physics engines were designed around the idea that one run through the main loop is 1/60th second.

This also explains why SNES games slow down when there are a lot of enemies on screen instead of getting choppy framerates - if the main loop ever takes longer than one frame, the physics engine does not correct for it.

Games that appear to have visual flaws induced by low frame rates are usually suffering from separate issues. Animations may be choppy because a game without a lot of storage space would find it very budget-friendly to use fewer frames. Movement may seem jerky because multiplies and divides were pretty computationally expensive, and there was no hardware floating point. A sine calculation was usually limited to 8 or 16 bit fixed-point arithmetic, same with square roots.