Game physics still tends to go "boink", because with impulse/constraint collisions, everything, including large, heavy objects, bounces instantaneously. Stuff flying apart, though, is rare now; most systems drain the energy out of a system when they detect that happening. It's physically wrong, but looks less awful.
I used to work on this stuff. I solved the "boink" problem for articulated rigid body physics in the 1990s, but couldn't make it work in real time on 100MHz CPUs.
Most games are using position based dynamics now (see Nvidia PhysX) so there isn't even a variational principle to arrive at the system from an energy. Just a constraint satisfaction problem with a weak notion of momentum coupled in.