Regie translates to "direction" or "directing," as in the artistic control of a film or play. It's a less common word to find in everyday song lyrics, making it stand out.
In the song, Johannes Oerding uses it metaphorically when he sings, "So wie 'n Film ohne Regie" (Like a film without direction). This powerful image conveys a sense of being lost and without purpose, highlighting the profound impact of the person's absence.
Johannes Oerding builds "Wenn Du Gehst" ["When You Leave"] out of a list of things defined by what they're missing: an old man without his cane, a plane without wings, a beach without sand. Verse one turns that list toward someone else: "Der Mensch ist irgendwie komisch" ["People are kinda weird"], he sings, because they forget what they have until they're suddenly alone. Verse two hands the exact same list back to the singer himself — guitar without strings, song without melody — swapping "Der Mensch" for "Ich bin irgendwie komisch" ["I'm kinda weird"]. Both verses arrive at the same plain confession, "Weil ich eigentlich schon weiß, du fehlst mir" ["Because I actually already know, I miss you"], so the song makes its point through repetition before the chorus ever says it outright.