KMOX-1120 has a powerful signal, and the New York Times story is correct in noting that the St. Louis Cardinals' huge fan base is in part due to KMOX's signal.
Until 1958, St. Louis was the westernmost city with a Major League Baseball team, so I suspect that the Cards' fanbase, thanks mainly to KMOX, probably stretched as far west as the station's nighttime signal could probably go. I suspect it probably could have been heard as far west as California under the right conditions.
Much like the Toronto Maple Leafs hockey team used to have a huge fanbase across all of Canada (except Quebec) and the northern United States (outside of the Boston, New York, Detroit and Chicago areas) thanks to the powerful nighttime signals the old CBC AM Radio stations had, the Cards likely had a huge fanbase across the Midwest (west of Chicago and Milwaukee), the Great Plains, the Mississippi Valley, parts of the Southeast and Southwest, thanks to KMOX.
These areas (excluding Minnesota) probably also became big hotbeds of interest in the St. Louis Blues hockey team in its early years in the NHL (after the team began play in 1967) thanks to KMOX's broadcasts. It should also be noted that the Blues made the Stanley Cup Finals in the first three years of their existence----thanks to the fact that the "best" of the "New 6" would play the "best" of the "Original 6" in the finals. But in 1969 and 1970, the Blues became a legitimate championship contender, which no doubt benefited the team and KMOX. And having Dan Kelly (after 1968) on play-by-play certainly didn't hurt.