According to R' Samson Raphael Hirsch, in his commentary on these verses, the point of this altar was to represent a counterpoint to Amalek, and the launch of an eternal defensive war against what Amalek represents. Where Amalek tries to destroy, Moshe builds. An altar is an inherently peaceful structure, devoted to God's service, and divorced from even a hint of weapons of war, as we see in Exodus 20:22:
וְאִם־מִזְבַּ֤ח אֲבָנִים֙ תַּֽעֲשֶׂה־לִּ֔י לֹֽא־תִבְנֶ֥ה אֶתְהֶ֖ן גָּזִ֑ית כִּ֧י חַרְבְּךָ֛ הֵנַ֥פְתָּ עָלֶ֖יהָ וַתְּחַֽלְלֶֽהָ׃
And if you make for Me an altar of stones, do not build it of hewn stones; for by wielding your tool upon them you have profaned them.
נס doesn't mean "miracle" so much as "banner." It's the sign that tells the fighters where to go. So, while the Israelites will fight Amalek every time Amalek attacks, it will not be offensive war for its own sake, but war to defend God's ways on Earth, as directed by God: "God is my standard!"
In the next verse, two words are incomplete: כס is short for כסא, or throne, and יה is an abbreviated form of God's name. According to R'Hirsch, these contractions represent the dimunition of the rule of God over the world represented by Amalek. Amalek asserts that humans should reject Godly morality in favor of the pursuit of might and power. So, as long as some humans follow this Amalekite philosophy, they are rejecting God's rule, and the power of His throne (יד על כס) is incomplete. As long as that's true, the struggle against Amalek will continue, kept up by those who March under "God's standard."