I get that proton remnants have no effect in the Oxy plane, thus the amount of momentum in this plane that vanishes due to momentum conservation is considered to be somehow related to the presence of dark matter.

This is a very good summary. Just to emphasize: we measure the total momentum in the transverse plane (Oxy) and what is missing so that the sum of all contributions from all particles is called the "missing transverse momentum". This could of course come from neutrinos, but if the amount is large, this may be connected to dark matter. At the end, it is a matter of confronting predictions of the Standard Model to data and see whether we have room for dark matter or not. So far: nothing non standard :(.