In 1901 Alex promoted a series of competitions with Harry Vardon, a personal friend. A.G. Spaulding, who acquired the Wright & Ditson Sporting Company, hired Alex to encourage Vardon to come to the U.S. and promote a series of exhibitions. After playing 4000 holes throughout the U.S. Alex held his own. But this was not a competition, these exhibitions were designed to promote the game of golf in the U.S. Indeed it did promote the game. In Scotland and England in the 1880's, when young Alex traveled to the New World there were only about 30 golf courses in the world, mostly in Scotland. Alex played everyone of the courses in competition from 15 years of age onward. He played against every professional that played the game at that time and beat every player. His young competition concluded when at 20 years of age he scored the first 72 ever shot, setting the bar to it's present level. He was at the height of his game, time to move on and play against new players and new courses in the new world.
When Alex died in 1942 he personally played on 2,400+ golf courses in the United States alone. When Alex came there were no players of the game in the U.S. He tirelessly promoted the game so much that when he died there were over 5 million players. So back to the question, did the Vardon/Findlay matches promote the game of golf? Outstandingly so.