Much of the post comes from a general assumption that the goal of computer graphics is primarily to replicate how a camera sees the world around it. Thus I think it's easiest to start from the idea of real world light entering a digital image sensor. Light in this setting is not continuous! Each subpixel in an image sensor acts as a photon counter. One photon hits the sensor, the count ticks up by one. There's no question of being able to perceive the values between 1 and 2 because they don't even exist. Either the sensor counted one photon or two. If you were going to literally create a digital camera that can process the entire world, you need 20 bits to count up to a million photons without losing any along the way. So if you were to build the hypothetical rendering pipeline that works on "real world" data about the scene, that 20 bit value would be the input.
As a practical matter, nearly all modern games store lighting levels internally in floating point, in arbitrary units chosen by the developers. Lighting pipelines are not integer based, but they're linear and not perceptual. The conversion to perceptual 8 bit (gamma curve) happens as part of the tone map stage. Doing things in floating point physical units is a better idea than the photon counter anyway, but the line you're confused about was really written with idealized cameras in mind.
(Technically an image sensor is an analog device and the voltage increases with each photon detection by an increment that is subject to noise of all sorts and pre-amplification before hitting ADC. Don't jump me on the photon counter thing.)