cyber_kinetist parent
The most common integration method in physics engines for games is semi-implicit Euler, which the article is implying from the source code. I think you are confused with explicit (forward) Euler, which nobody really uses.
For those not in the know (I had to double-check myself), the difference between explicit and semi-implicit Euler is simply the order in which position and velocity are updated.
Explicit updates position with the old velocity:
particle.position += particle.velocity * dt;
particle.velocity += acceleration * dt;
particle.velocity += acceleration * dt;
particle.position += particle.velocity * dt;