Defining contrast ratio and dimming ratio in a LED driver
Based on some datasheets and whitepapers, I get the idea that having the CR defined as in the EDN article was, surprisingly, wrong. Hence why I wasn't understanding and why I asked here: I was assuming it was correct and that I was missing something. I try to explain.

The problem was that it was defined as 

\$ CR = \frac{1}{t_{onmin}} \$; where 
\$ t_{onmin} = t_d + t_{su} \$

The Duty Cycle was defined as \$ D_{min} = \frac{t_{onmin}}{T_{pwm}} \$.
And in the CR seems to not care about the PWM period, which is weird, since the text on the EDN article clearly says that is dependent on it. So starting to think and overthink about it (also in the chat under the OP), I get to the idea that the CR must be related to the PWM period, which is the maximum achievable duration in one cycle, i.e., 100% of Duty Cycle (DC). So:

\$ CR = \frac{T_{pwm}}{D_{min}} : T_{pwm} \$; where after normalizing this ratio became:

\$ CR = \frac{1}{D_{min}} : 1 = \frac{T_{pwm}}{t_d + t_{su}} : 1\$ 

On the ILD6150 datasheet, for example, under contrast ratio chapter, they show the same definition.

Regarding the Dimming Ratio definition instead, I think here is the same, since is the ratio of the highest Duty Cycle over the minimum. Since the higher Duty Cycle of 100% means \$ D_{max} = \frac{T_{pwm}}{T_{pwm}}\$ and \$ D_{min} = \frac{t_{onmin}}{T_{pwm}} \$, their ratio is:

\$ DR = \frac{D_{max}}{D_{min}} = \frac{1}{D_{min}} \$

Which is exactly the same thing as Contrast Ratio.

Any further correction on this is more than welcome.