It is interesting that they refer to the simulation system as 'Verlet Physics' -- that sort of constraint satisfaction system is called 'Position Based Dynamics' in most of the graphics lit. This type of system is also used in Maya's Nucleus and NVIDIA's PhysX. [1] is a nice overview.
They're calling it Verlet physics because they're using a Verlet scheme for integration - which is a relatively elegant approach if you don't ever need velocities.
But it isn't really verlet, I don't think it will converge like a 'standard' verlet implementation with constraints (like molecular dynamics cats use) - the effective stiffness of the objects here is dependent on the time step.
[1] http://matthias-mueller-fischer.ch/publications/STAR2013.pdf