Nonlocal in kinetic theory means you substitute local variables like the heat flux: q(r,t)=ec(r,t)*v by a non local variable wich usually involves an integral kernel. One needs to do so if the particle distribution function has a long tail in the high energy domain. Particles traveling at hight velocity do have a non negligible effect on the heat flux, even if they are few. But their hight velocity means that between t a t+dt they have travelled a substantial distance. So to take them into account you need to widden the local operator to a non local one.
Electron transport in the divertor plasma ans scrape off layer in Tokamaks are typically non local.
I haven't read both papers you've linked, but in the first one: "Solution of the Dark Matter Problem in the Frame of the Non-Local Physics" Pr Alexeev first generalizes the Boltzmann's equation by introducing a term that takes into account the finite size of the kinetic cell (small enough to be considered a point when looked from a macroscopic point of view, but large enough to contain a sufficient number of particles to introduce a continuous distribution function). This extra term is non local in the sense that it adds an integral operator to the collision Boltzmann's operator. Then The author takes the hydrodynamical limit to derive fluid equations. When ones uses these new set of equations to cosmological problems, one can deduce the observed effects that are up to now attributed to dark matter. But the extra non local term avoid to introduce exotic matter. This term is not due to a new physics but to a better treatement of the kinetic equation: one just drops the point size hypothesis of the kinetic cell.