빠지다's meanings may be divided into two broad groups.
1. fall into a pit, a bad condition, emotion, habit, etc. usually against one's will.
- a 구덩이에 빠지다: fall into a pit.
- a 도박에 빠지다: fall into a gambling habit.
- a 사랑에 빠지다: fall in love.
- a 어떤 사람에게 빠지다: fall (amorously) for someone.
- b 신중해 빠지다 (=지나치게 신중하다): be overly cautious.
- b 느려 빠지다: be excessively slow.
(빠지다 in the #b sense is only used in familiar speech. It can sound rude.)
2. comes out of a pre-established state, including physical setup as well as figurative things like a meeting, etc.
- a 못이 빠지다: A nail came out.
- a 이빨이 빠지다: a tooth falls out.
- a 얼이 빠지다 / 정신이 빠지다 (= 얼/정신이 나가다): be distracted; lose one's mind.
- a 기운이 빠지다: lose strength/vigor.
- b 그룹에서 빠지다 (=탈퇴하다): withdraw from a group.
- b 모임에 빠지다 (= 참석하지 않다): doesn't show at a meeting (where one is expected).
- c 이익이 빠지다 (= 남다): a profit comes out of a business (사업에서 투자 금액은 빠졌다).
- d 돈이 빠지다 (= 모자라다): some amount is missing (돈이 만 원 빠진다).
빠지다 does have a lot of meanings making it difficult to grasp all the usages (the #a and #b are the basic ones).
As for the website (sixmoment.com), it is a potpourri of blindly collected pictures with "빠져가지고" in caption.
The top picture has "#얼 #빠져가지고" (얼빠지다 = 얼이 빠지다), which means "lost my mind" to the awesome arts there.
The next picture mentions falling for someone, so the collection doesn't have any consistent theme.