While war films are often also action films, they don't have to be. Lots of great war films are about the psychological effects of war, or about the effects of war on the population back home. With Platoon, war is front and center, even when, strictly speaking, there's no action.
The scenes that take place at camp in the drug den, for example, depict war just as much as the actual battle sequences do. Good war films show that the "war" among the troops of the platoon, and the battles, psychological and otherwise, they individually fight (with fear, drugs, alcohol, etc.), are just as important as the explosions and shooing more typical of the battles against the enemy.
Like most war movies, Platoon is definitely an action film. There are several huge firefights, explosions, fires, helicopters, and all the other bells and whistles we associate with war films, and with action films more generally. Many of the film's major turning points take place during battles (Elias' death, for example, or Taylor's killing of Barnes).
Unlike lots of action movies, however, the action sequences in Platoon are designed to induce horror, not excitement. They show us how awful "real" action can be, and to dramatize its psychological effect on the participants.
The bickering between Elias and Barnes over how to conduct the war in Vietnam, the "civil war" among the troops of the platoon, and the politics of leadership are the hallmark of great drama.
On top of all that heavy drama, there's Chris Taylor's emotional journey over the course of the film. He starts out as a green, innocent, naïve soldier, a guy who voluntarily dropped out of college and enlisted. After witnessing all the horrors of war—illegal killings of civilians, fragging, torture—he's had enough. By the end, he's a hardened soldier, one willing to frag one of his superiors (Barnes) because he knows he can get away it. Drama all the way.