I'm not aware of any research that establishes how it affects dental plaque, but there is research that suggests it dissolves arterial plaque, which is, in part, made of calcium (hence the cardiac calficiation score), and there is sufficient information overall to formulate a hypothesis on why it would work for dental plaque.

The general effect of vitamin K2 is connected with vitamin D, calcium and magnesium. Vitamin D upregulates calcium utilization, and has been shown to cause conditions of excess calcium e.g. hypercalcemia when cofactors are not present (e.g. magnesium or vitamin K2 deficiency).

While magnesium has a modulating effect on calcium absorption and utilization, vitamin K2 has a stronger effect whereby it causes calcium to be pulled out of inappropriate places (arteries, and apparently teeth) and moved towards appropriate places (bone and other tissues).

Dental tartar typically consists of biofilms made in part with calcium that shield the bacteria from the immune system (consider the term "dental calculus," which has the connotation of calcification). Presumably, vitamin K2 pulls the calcium from the biofilm, which causes it to collapse.