Final answer:
While the text provided doesn't directly answer the question about a 1904 England-Scotland badminton match, it suggests the possibility of such an event since international participation in badminton championships was occurring around that time.
Step-by-step explanation:
The information provided relates to the development of college football and other sports during the late 19th and early 20th centuries but does not specifically address the existence of an England-Scotland badminton championship in 1904. However, through independent historical knowledge, it can be confirmed that the first official All England Open Badminton Championships were held in 1899, and this competition did include international participants over the years, suggesting that a match between England and Scotland could have occurred in 1904. Nevertheless, the original text primarily highlights the progression and popularity of college football in the United States, along with the creation of basketball by James Naismith.