It should be obvious that there are no 8.7 × 10^45 possible chess moves from any chess position. All pieces have less than 32 moves per piece and 19 pieces means less than 608 moves.

No, they do mean possible moves and they don't mean maximum length game. There are on the order of 10^45 reachable chess positions. The article did not say that was the number of moves from one position. The article says 218 is the maximum number of moves from one reachable position--it's the whole point of the article!