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.
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.
If you're doing semi-implicit Euler that's pretty good, per gaffer's article, semi-implicit Euler has the advantage of being symplectic, i.e. its an integration method that conserves the total energy of the system you are simulating (energy conservation! physicists love it!).
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!
Let's bear in mind that Australians call their best friends Good Cunts, and try to take it the best possible way :D I don't even disagree with him, it's just too easy to do better.
The friction/damping term you've added is absolutely necessary to counteract the systematic energy gain from Euler integration, and with better integration, you need less / no unphysical damping, leading to more of that delicious chaotic behaviour we're all looking for.
You can even cheese this with infinite amount of computation if you wanted to do it braindead style (which is still super instructive!), by just repeating the step function with a scaled-down dt until the position components agree to within some tolerance.
The rest is an incredibly deep rabbithole, which I've been enjoying since decades :D
