What a fabulous old photo! Obviously, these young people were flying high in Comanche, Texas in 1903, a time when few people had the time to stop their work for play.
While I was first tempted to think this group was playing tennis, I believe it must have been badminton or something related to it. Notice the sand under all of their feet? This “court” was, I assume, located on the Cunningham estate, where later Bill Clemons would build his house.