So I get that all energy missing in the transverse plane is obviously measured and then linked to the existence of dark matter, providing scientists with the ability to create a dark matter model of some sort?

Not necessarily. Neutrinos are also invisible. Also, mismeasurements induce fake missing energy too.

To summarize, a large amount of missing energy could be related to dark matter, but the Standard Model and experimental effects contribute too (they make the background).