Examining them independently first of all:
The first-person narrative
Is defined by the use of personal pronouns, 'I' and 'my' it creates the effect of seeing and experiencing the events of a text through the character's or narrator's eyes, like in your example with I see. Furthermore, it evokes a distinctly personal angle from the text.
Is a subjective viewpoint, we become one with the narrating character as we only see and interpret events through the narrator's perspective and we do not gain an objective insight (this is sometimes a criticised quality to first-person narrative as it is often considered unreliable, as the way the narrator sees an event may contradict other characters' experiences).
Deepens the reader's insight and emotional understanding of the character - we get to know the inner thoughts and emotions of a character which would otherwise be impossible with third-person narrative. (reference) This is also a great asset in the case of bildungsroman novels, as we gain a deeper understanding of the protagonist's development, since first-person shows psychological as well as external maturation (third-person often only demonstrates the latter). Ultimately, it helps to evoke empathy from the reader towards the narrating character; third-person narration is often much colder and detached.
First-person can (this is not always the case) also be used as an outlet for the author to broadcast their personal opinions when they appear to assume the voice of their narrating character. This can be seen in Charlotte Brontë's Jane Eyre, where she speaks through Jane criticising elite society's attitude towards governesses (reference: Susie Campbell, Critical Studies: Jane Eyre)
- Above all creates immediacy, the events are described as occurring in the moment that we read it.
Using both present tense and first-person narrative together you can apply and converge all the effects of first-person narration to the immediacy of the present tense. It creates a more powerful exciting atmosphere than past tense first-person. (reference)
It conveys the spectacular effect of landing the reader in both the actions and emotions that the narrating character is experiencing. The 'in the now' impact of the present tense enable the reader to undergo changes unexpectedly like the narrator without the hindsight of past tense first-person. The use in the text you gave as an example is particularly effective to this degree as it is about a battle - the reader feels all the fear, suspense and danger that the soldier is feeling, like the cinematic effect of a camera mimicking a characters visual field and movements.
(The issue with this is that it can occasionally feel monotonous in a quieter environment as the narration does not shift from the immediate).