That’s true, the path integral of water viewpoint is what you would ideally want, especially if you were trying to explain just how far you could see on a given day, or why the top of the mountain is usually clearer than the foothills below (more water and dust at lower altitudes).

In fact, because you do care about scattered light coming from anywhere, you can’t just look at the line between your eye and the mountain. You need to know the whole spatial distribution, including stratification (e.g., rainbows). Indeed, some of those photons are scattering multiple times before they enter the light path from your eye to that green tree (double rainbows). Radiative transfer modeling is hard!

But column H2O is a well measured quantity for which there are off the shelf data that do show and explain the seasonal effect that OP mentioned (as the map shows). Basically, the gross, hundreds-of-kilometer monthly-average H2O that’s in that map is the constant factor out front of the light-path integral that is the “right thing” to use.