It's been known since the 1930s that it's totally dependent on mass, that's not something that was discovered last week. An older book I have that talks about the mathematical derivations (doesn't actually show the math but explains it) says that up to 1.4 solar masses, your star will become a white dwarf. (This is the Chandrasekhar Limit, named after an Indian astrophysicist who derived it it 1930.) From 1.4-3.3 solar masses, your star will become a neutron star. From 3.3 solar masses on, your star will become a black hole. Maybe the difference between the 3.3 and 2.16 solar masses is that 3.3 is for a normally shining star and the 2.16 is after it has exploded in a supernova and blown off some material.
Bottom line: conceptually, there's nothing new here except for a few numbers that are suspect. Must be a slow day at Popular Mechanics. The title Astronomers Find Mass Limit for Neutron Stars Before Collapsing Into Black Holes is a complete crock, this number was known back in the 1930s and was refined in the 1960s when calculating differential equations and integrals with computers became a lot better. These scientists may have tightened up some of the numbers using some new methods but they discovered something new? No, that's a total crock.
Good post. I was immediately wondering the same thing. This whole article makes this sound like something new.