Human vision is non-linear, but it is not logarithmic. What it does have is several different mechanisms of adaptation which allow it to respond to very dim or very bright contexts. Some of these adaptations take 30 minutes or more.

But what we are talking about here is the wavelength-responses of a particular type of cone cell. Individual cone cells are activated when some photon excites a little protein and causes a chemical reaction. You can read about the details here https://en.wikipedia.org/wiki/Opsin

The spectral sensitivity charts we are talking about here show more or less a summary of how likely that signaling process is to happen for a particular type of cone cell for light coming in at a particular wavelength. To figure out the eye’s overall cone response to some particular light source, you can more or less take the spectrum of the light source, multiply by the spectral sensitivity of the type of cone cell, and then integrate. Notice that that part of our process is linear in terms of the charts we are talking about.

The non-linear part has to do with various types of adaptation which attenuate or discount those cone sensitivities more or less uniformly across wavelengths (for each cone). This doesn’t suddenly make the left part of the long-wavelength cone response more relevant.

Let's assume you're correct, and that the more-or-less logarithmic aspect to human vision is inconsequential here, and also that the hump in absorption around 410nm by the red cones is also irrelevant. How would you explain the human perception of violet light as a purple colour, then?

By “violet light” you mean a 400 nm laser or something? Or a blacklight? https://en.wikipedia.org/wiki/Blacklight

In normal circumstances (say, daylight surroundings), a moderate amount of light at very short wavelengths won’t look like much of anything at all, bluish–black, because the cone cells (especially L and M cones which determine red–green response) will be getting much more stimulus from other wavelengths.

If you go to a completely dark room, let your eyes adapt, and look at a blacklight, then you are right that you are at that point going to see it looking purplish because the L cones are stimulated a bit more than the M cones for those wavelengths, and other wavelengths are entirely absent. But this is a really weird edge case for vision.

The first sentence in the wikipedia article says: "A blacklight [...] emits long-wave (UV-A) ultraviolet light [...]."

Why does it say "long-wave" when UV is short-wavelength ?

Because the light that blacklights emit is on the longer end of the possible UV wavelengths. This is what the UV-A means. There are also UV-B and UV-C with shorter wavelengths.