It is definitely far, far more than just what particles exist. The Standard Model describes how those particles interact with via the three forces other than gravity. The particles themselves are modeled using quantum fields and the properties of particles arise from operators on those fields. Those operators don't work unless the field is continuous.
The operators will have a spectrum which describes how the corresponding observable is quantized.
That's not really ELI5, but remember learning derivatives in calculus? Just like you can't take the derivative of a function which isn't continuous, you can't use the Standard Model if spacetime isn't continuous.