I just followed the link, to read the explanation under Donate.End-game conditions are checked at the end of each player's turn. So if a player buys Donate and then empties the Provinces, the Donate effect will not occur.
Conversely, if two piles are empty and a player buys Donate, and uses its effect to trash Hunting Grounds, thus emptying the Estates, the game will not end until the end of the next player's turn.
The first one makes it clear what Stef said. If the game is over at the end of a turn, then no Donate effect. And the card makes it clear that its effect happens after the turn [is over]. But, given this, the second Rules Clarification seems bizarre to me. I play Donate, trash Hunting Grounds, empty the third pile of Estates . . . BUT, that does NOT end the game??? The next player gets an extra turn?
What is the rationale for this exception? Are there other edge cases where a game should be over (Prov empty; 3 piles empty) but another player gets an extra turn?