This connects to the intensity equation often used for sound in physics. The equation is I=P/A (I=intensity, P=pressure, A=area). In this case, since we're looking at a circle of radius r, I is inversely proportional to r^2 (since the area of the circle is pi * r^2). This is where the relative intensity formula on this slide comes from!
Does this mean that our intensity is always defined at 1 unit away from the source (r=1)? Doesn't this become arbitrary if we change units or scale? By this model, couldn't we get theoretically infinite intensity as r -> 0, or do most graphics applications that our light is the unit sphere?
You would get theoretically infinite intensity as r->0. The resolution is that light never comes from a single point in the real world (aside from small discrete numbers of photons being produced in individual interactions with other particles, which don't define an intensity since we can't properly average the rate over time), the object producing the light has some nonzero volume.