I’m just curious, but the definition sounds like distinguishing between religion and faith not exactly religion and mythology.

No, the definition is distinguishing between types of faith, not between religion and faith.

Animism or shamanism doesn’t always have overarching dogma to teach nor actively ask other people to believe in them.

Okay? I'm not sure what the point of this line is.

Ancient Greek people did some rituals and sacrifice, that practices they did doesn’t count as religion?

No. The mistake that people keep making in this thread is conflating mythology and religion. They are two very distinctly different things but that does not mean that they are mutually exclusive. There is Christian mythology that is part of the Christian faith. Note the use of 'faith' and not the use of 'religion'. There is a reason that these terms are frequently used when talking about what are colloquially called 'religions'. Religion is one part of the faith. Mythology is another part of that same faith. It is important to recognize the difference between the two but that doesn't mean that they aren't related.