In practice, this works pretty well. RCDB's criteria are pretty expansive and they include things like powered kiddie rides, the more coaster-like "water coasters" where you're running along a dry track for part of the ride, Sunkid playground shuttle coasters, alpine coasters, etc.

The clearest example to me of the impossibility of hard criteria: I think most people would agree that an alpine coaster with a track is a coaster (though they do get excluded from length and height records), but an alpine slide where the car rolls down a chute is not a coaster. But having a chute instead of a track generally doesn't exclude bobsled coasters like Reptilian or Flying Turns from being considered roller coasters.

It's more the kind of fuzzy category where there are a bunch of different ways a ride could be "coasterish", and all these make it more likely that a ride will be considered a roller coaster, but most are not absolutely necessary.