He is widely regarded as one of the most important figures in the amateur beginnings of Atlético Madrid since he was one of its founders in 1903, a vice president between 1903 and 1905, and the club's first-ever patron.
[2] He was an all-round and versatile athlete, playing both football and field hockey for Atlético when necessary, running foot races, and even coaching tennis.
[6] During his youth, Rodríguez Arzuaga traveled a lot, and in one of his trips, to London, he discovered the game of football and developed a deep interest in it.
[8] On 8 November 1907, Rodríguez Arzuaga started in a friendly match against Club Español de Madrid, scoring the opening goal in an eventual 2–0 victory.
[4][9] He paid for the expenses, trips, referee fee, the trophies, and soon the kits too, because, in January 1911, he approached Juan Elorduy regarding the red and white shirts that he had brought from Southampton to Athletic Bilbao, so that he would bring them from his home in Bilbao to Madrid, stating "When you return to Madrid after Epiphany, you can bring them with you, I will pay for them all".
[4][7] Atlético played its first game as a red and white team in the second edition of the Copa Rodríguez Arzuaga against Sociedad Gimnástica on 22 January 1911, which ended in the latter side withdrawing.
[2][4] The construction began at the end of 1912, and the project was carried out only thanks to the financial contribution of Rodríguez Arzuaga, patron of the club, who put up 30,000 pesetas (which at the time represented a fortune) to prepare the land and pay for the 600 linear meters of wood used in the fenced.
[2] Finally, on 25 October 1930, a group of 50 venerable "colchoneros" gathered together and decided to create a club that they would call "The 50", of which Rodríguez Arzuaga would be its first partner.
[2] On 11 November 1909, Rodríguez Arzuaga appeared on the first board of directors of the Spanish Football Federation, being elected as a member alongside the likes of Narciso Masferrer and Joan Gamper, under the presidency of Pedro Neyra.