Definition of elementary particle 
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Why are atoms particles? 

According to wikipedia an elementary particle or fundamental particle is a particle not known to have substructure. 
Moreover, I've learned that such a particle satisfies the Dirac Equation, and this is a mathematical condition to be respected to deserve the appelative "elementary", because among the hypothesis Dirac used there is a limitation in the degrees of freedom. 
One of the proofs of the non-rotation of the electron, is the negative argument which negates that the spin represents a real-space rotation of a sphere (the electron), using its gyromagnetic factor and the limit velocity $c$. In this sense, the electron doesn't have any additional spatial degrees of freedom.
At last, in QFT, elementary particles are assumed to interact in point-like collisions. 
Therefore, I'm wondering about the deepness of the concept of point-like particle. Is this just a model, an approximation, or when we deal with QFT and similaria we relate to this concept the real existence of point-like particles?
 A: The reply of David Zaslavsky to the question linked by Luboš Motl in the comments above answers "why are atoms particles", paraphrased:
" In practice, I would say a particle is anything that can be treated as a single,  small object with  specific  mass and center of mass coordinates (x,w,z,t) and (p_x,p_y,p_z,t) in four vectors. This means that whether an object is considered a particle depends on the framework you are examining it".
For the subset "elementary particle" the center of mass coordinates coincide with the location of the particle as a whole, thus no substructure is posited.
History of physics tells us that "elementary" as a concept changes continuously  as better ways of studying nature are found. At the point we are now the Standard Model ( note "model") assumes as elementary 

at least the particles in the table. The standard model is a shorthand for all the known data from particle physics up to now because they follow it to first order.
Thus the  hypothesis that they are elementary is fully supported by the data up to now. 
QFT works for point like particles but theorists are working hard on string theories where the basic idea is that particles instead of points are strings described by functions including the four dimensions we know but at least 6 more dimensions; they are vibrations on stings, which are non local. If one of the models based on these theories is validated in the future by experimental data, it will include and supersede the standard model.
So yes, in physics we are always talking of models, but, and it is a big BUT, based on experimental data for validation.
