How does the hero deed at Weathertop constitute mortal combat?

The battle at Weathertop is an episode that occurs in J.R.R. Tolkien’s The Fellowship of the Ring. Weathertop is a hill midway between The Shire and Rivendell, where the hobbits stop for a night’s rest. During the night, the Nazgul find the hobbits and recognize Frodo as the ring-bearer. Frodo has a desperate skirmish with the Nazgul king during which he is wounded by a cursed Nazgul blade. Soon Aragorn emerges to save the hobbits.
Though Frodo and Aragorn both act heroically, it is Frodo who puts the most on the line to keep the ring from the Nazgul. As the evil blade pierces Frodo’s shoulder, Frodo manages to slash the Nazgul’s cloak with his own sword. Frodo’s wound is grievous, but he proves that, in the heat of battle, he is able to face and land a blow against one of the most powerful and evil creatures in Middle Earth.
The skirmish between Frodo and the Nazgul could be described as “mortal combat” insofar as Frodo fights for his life and for the quest to destroy the ring. To be fair, the same cannot be said for the Nazgul, a powerful and possibly immortal being. As a hobbit, Frodo is accustomed to a safe and comfortable life, which makes his bravery at Weathertop all the more remarkable.

Tolkien, J.R.R. - The Fellowship of the Ring. New York: Del Rey; Reissue edition (August 12, 1986)
https://thefairytaletraveler.com/2015/05/14/real-inspirations-for-middle-earth/