The number of golf courses in the 19th century is often overestimated, even for Europe. In 1888 there were only 138 courses in the UK (Scotland 73, England 57, Ireland 6, Wales 2). But starting in the 1890s about 100 courses per year were built right up to World War I.
The numbers for the US, that Walter Stephen quotes in his book, are actually from Cornish & Whitten (as are the ones above).
Ulrich