When you see a sentence like, "...whereas the lower ultraviolet, visible light (including laser light), infrared, microwaves, and radio waves are considered non-ionizing radiation." the use of the verb 'considered' often means that a convention has been adopted or a judgment call made.
In this case, although there are certain conditions under which visible light can cause an electron to be stripped from an atom, just like what would happen if a gamma ray or an x-ray did, the judgment is that the ionizing effect of exposure to visible light is nowhere near as hazardous as uncontrolled exposure to x-rays or gamma rays, which can be downright lethal.
Visible light is naturally present due to the sun, whereas x-rays and gamma rays, which are also produced by the sun, are not normally present in large amounts on the Earth's surface due to the protective effects of the atmosphere. Exposure to non-lethal amounts of x-rays or gamma rays can lead to damage to one's DNA and assorted mutations, where this is not the case with exposure to visible light. [The tanning of the skin is the body's protective response to exposure to UV rays produced by the sun, and naturally, there are warnings against overexposure to UV light (even from tanning beds) and suggestions to liberally apply sunscreen when outdoors for lengthy periods.]
It's also a practical consideration as well: imagine if a flashlight sported one of those cool radiation warning signs
and you needed to wear a radiation suit every time you used one, or have a radiation safety officer present to decontaminate you after you were done using the flashlight.