In my opinion, the present-tense in A present-tense record refers to the "narrative present", also commonly known as historical present, which "refers to the employment of the present tense when narrating past events.
The historical present will give the audience "a sense of immediacy, as of a recurring vision", so CopperKettle's suggestion that the film would give the feeling of the "present" is not very far off. In fact, I believe that the film used everything to achieve the effect of the "present".
I've checked it on IMDb. According to IMDb, The Battle of Chile: Part I (1975)'s language is Spanish. I can't say anything much about Spanish, but according to The Guardian, the film appeared to be voiced over in English in the present tense (i.e. the historical present):
Everything about the style of the film - the restless camera, the short scenes, the present-tense voiceover - indicates that its makers suspected this as well.
which sums up the whole sense of "A present-tense record" quite well.