So that source draws a line between cosmological redshift and doppler redshift that is so misleading I'd say it's wrong. They are in fact equivalent [1] and basically just depend on your reference frame.

Check out the wikipedia page on Hubble's Law [2] for more.

[1] https://arxiv.org/abs/0808.1081 [2] https://en.wikipedia.org/wiki/Hubble%27s_law