Since the world was covered mostly by water, only a strong navy would enable a nation to "project" it's military might (armies) across the globe.
If a nation didn't have a strong navy, they could not compete in the world's Arms Race; they could not be a major player, just part of the audience sitting on the side lines.
What good is a strong army, if it can't reach an enemy to conquer (because of an ocean)?
Mahan influenced the Kaiser & the Tsar of Russia to build up their navies. Britain already thought along Mahan's lines. The Kaiser slyly eliminated his cousin Nick of Russia, by getting him into a fight with Japan in 1904...which effectively caused the loss of 2 of Russia's 3 battleship fleets; thus removing him from the (naval arms) Race.