> There is no reachable chess position with more than 218 moves.

"no more than 218 possible next moves" would be a lot clearer...

> By checking all approximately 8.7x10^45 reachable chess positions?

That's a large overestimate.

https://github.com/tromp/ChessPositionRanking accurately estimates the number of legal chess positions at ~4.8x10^44.