Given the context of the poem, the "he" who plunges at the narrator is a specific person.
Before the stanza about the "he" coming towards the speaker, the speaker has told us the story of a specific gas attack on a French battlefield during World War I. Everyone quickly puts on their gas masks, except for one man who is too late. He breathes in the burning poison gas. The speaker describes seeing him flounder and go down, as if he is drowning in a green sea of gas. Then, in the next stanza, the speaker describes how in his dreams, this same man "plunges" at him.
That this is a specific individual and not simply a universal "he" referring to all the gassed men the speaker saw is reinforced in the next stanza. The narrator goes on to give a detailed description of the horrible way this man, thrown into a wagon, suffered from inhaling the gas:
the white eyes writhing in his face,
His hanging face, like a devil’s sick of sin;
If you could hear, at every jolt, the blood
Come gargling from the froth-corrupted lung.
Reading these stanza as a whole, we can see from our twenty-first century perspective that Owen is describing a specific traumatic moment in the speaker's war career. In his dream, the speaker relives the trauma and his feeling of being "helpless" over and over. We know today that trauma arises precisely from feeling helpless in a horrible situation, and this is what Owen depicts. He, through his speaker, uses the poem as a way to alleviate his own sense of helplessness by letting people know the horrors of war. He hopes, through this, to help prevent these horrors from being repeated.