모듬 게 너에게 닿기 위함인 걸 (모듬 -> 모든) => 모든 것이 너에게 닿기 위함인 것을
=> When it was all mean to get to/within you.
(It is 모든 게 너에게 닿기 위함이다 (It is all because I mean to get to you), connected with -ㄴ/인 것을 which creates a noun phrase in the objective case)
-ㄴ/인 걸 coming at the end of a phrase has roughly two uses:
1) direct the person's attention to a new fact mildly contradicting or correcting what they said.
2) (often in literary contexts) expresses one's own emotion (typically regret or remorse) about something, to the effect of "how/why did I not know/heed/act/remember it, etc.".
-ㄴ/인 걸/것을 normally makes a phrase or clause functioning as an object of a verb ("그 사람이 떠나려는 생각인 걸 몰랐다"), so if you end the phrase with it, the missing main verb creates an unresolved construct that relies on the context. In ordinary conversation, the missing part usually implies something like "You should know/act better, since [there is this new fact]". In the second case, the missing part can be any abstract and strong feeling, and creates a poetic effect about the great impact it has in the speaker's mind.