Gaffer (Glenn Fiedler, mentioned in the article) would also say, and I quote, "if you use Euler, then you're a bloody idiot" :) This simulation is using Euler integration.
I suppose I am a bloody idiot. This uses a simple delta time to smooth updates across frames rather than attempting something more formal. Based on the sister comment I think this is actually Semi-implicit Euler which still makes me an idiot. Eg, velocity += acceleration * dt; position += velocity * dt; Although, I add friction in a bad spot so maybe that is what you mean.
the particle motion in your videos looks reasonably natural, there's no obvious signs of particles seemingly gaining energy from nothing (apart from when they are perturbed by the mouse cursor), so as the resulting motion looks natural, what you are doing is fine and there's no actual problem you need to solve.
if instead of simulating independent particles you were trying to accurately simulate cloth or a deformable rigid body e.g. a metallic object crashing into something, where each node in your cloth / rigid body was a particle tethered to its neighbours, that might be a whole different can of worms and justify looking into RK4 or implicit Euler where you need to solve a big linear system of equations each timestep. but you're not doing that, so no need to overcomplicate things!