"Step right up" is a set phrase in English, combining a phrasal verb with an intervening adverb. "Step up" is a phrasal verb, while "right" is an adverb, used to denote totality or completion.
This is somewhat difficult to explain, because the preposition "up" is usually used to denote completion of a task, as in "finished up" or "cooked up". Often these prepositions are non productive for a linguistic point of view: finish already means "to finish", so "finished up" adds nothing to it. In "Step right up", we have a further expansion of this phrasal verb, by adding "right", an adverb of completion. So the phrase is redundant. It is also particular about its word placement: although adverbs are generally flexible in English, "step up right" or "right step up" are not comprehensible uses of this phrase. While there are many phrasal verbs that take objects1 between the verb and the preposition eg: "I filled it up", "step right up" is an example of where an adverb has a fixed place in a phrasal verb.
All of that is something that you already know, but that you didn't know that you knew, but now you actively know it. Also, something that would be a matter of difficult memorization for a non-native speaker.
1 Depending on whether the object is a noun or a pronoun, but lets not get ourselves into that.