Well, I should clarify that I don't know for certain what's going on, so some of this is a guess... hopefully it will be clarified eventually.
But we can get the following things from this chapter: At least from the perspective of the Prince and the White Rabbit, these events are happening before what we've seen so far. We're being shown the Prince's first meeting with the original Alice he fell in love with. Presumably this is a flashback.
And, at least to all appearances, the original Alice he fell in love with is, in fact, Arisu. It could be that Arisu dreamed his way into the Prince's world before, but had no memory during or after the event because he entered through a dream... and, in his dreams, he is female.
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