Hitomi is at track when she gets a vision of Van and faints. She wakes up in the nurse's office to see her crush by her side, and they have a bit of a talk where she shows off her pendant. Despite her best friend's orders, Hitomi wants to run again and do it properly this time, so they go out in the evening, and Hitomi gets the same vision again, but this time it's actually real, and she runs into Van who had found his way across dimensions to end up in her world with a real (and poor CGI) dragon. Van fights the dragon, and then slays it and gets out its heart. Hitomi, having been caught up in the action, ends up being swept away with him to his world while her best friend and crush watch helplessly (her crush tried to grab her hand, but the pendant he was holding onto for her slipped away instead) as she's sucked into the portal and finds herself on Gaia. (It's actually important we see her crush because he looks like Alan, and that's why Hitomi gets caught up in a love triangle.)
The first episode didn't air on Fox Kids because it would've given boys the "wrong idea" this was a girls' show. That's literally it. It's the exact same reason why it is Kids' WB aired
Cardcaptors out of order.
EDIT: Might as well show this off, then. The Fox Kids' opening I think was done to show the abridgement of the first episode anyway to then lead into the second episode. But the show was pulled from Fox Kids' after about ten episodes because of low ratings, so yeah, American viewers had to get the DVD for the full story.