So it adopted an "as long as triggers for an event haven't been handled completely and are over, new relevant trigger effects appearing will also trigger" approach . This leads to a Hireling double played by Ghost at start of turn actually giving you twice +1 card that same turn.
So that would mean the "For the rest of the game" ability appearing during Champion's playing is existing and relevant at the time 'normal' "When you play an Actions card" triggers are checked at the end of Champion's resolution.
Your explanation of new abilities triggering is accurate, but it's not relevant to what I was saying. My point was that Champion triggers right when you play an Action card (before you resolve the Action card) but would be resolved after resolving the Action card. This means that when you play it, its own "rest of the game" ability is not triggered. Please take a look at what I wrote again, and also check out the post I linked to in the Strategy Forum.
I can add that this interpretation is in line with how things work in Dominion. First of all, it's certain that an ability can have triggered without being resolved while other abilities are resolved in the meantime. (Talisman and Haggler in play, buy a card. Both trigger, but one is resolved first while the other waits.) Then we can extrapolate this to how abilites set up future effects: Play a Charm, it has a "when you play this" ability (happening right now) which says "the next time you buy a card", which is in the future. It's set up when you play the card, but it happens later.
Enchantress should also be interpreted this way: It triggers when you play an Action card, but is resolved when you would resolve the Action card's play ability. (Lantern and Ways work the same way.) Royal Carriage also triggers on playing an Action card, but is resolved after
. I don't really see any other interpretation that makes much sense and is consistent (and I've been working on cataloging the timing in Dominion for a long time).