I would say that the compound 빠져들다 is the standard abstraction of 빠져 들다 (or 빠져서 들다). For 빠져 들다, 빠지다 ("to fall into") indicates how the subject does the action 들다 ("to get in(to)"). In 빠져들다, however, 빠지다 and 들다 do not have their entire meanings because nothing actually moves: Unlike 빠져 들다, there is no physical or real movement for 빠져들다.
Both 빠지다 and 들다 have the word "into" in their English meanings although they are just verbs, which could make you think that 들다 is unnecessary. But, when two words used together have very similar meanings, you should think of such use as emphasis as gaeguri mentioned.
I will give you some examples for 빠지다, 빠져 들다, and 빠져들다:
- 신발이 눈 속에 빠져 들었다 (not 빠져들었다 because 신발 is moved).
- 신발이 눈 속에 빠졌다.
- 나는 잠에 빠져들었다 (not 빠져 들었다).
- 나는 잠에 빠졌다.
- 우리는 그렇게 사랑에 빠져들었다 (not 빠져 들었다).
- 우리는 그렇게 사랑에 빠졌다.
There are a lot of compounds that can be understood in a similar way, but they may be abstraction of a phrase or, more generally, acceptance of a commonly used phrase as a compound without spacing:
- 뛰어들다 (뛰다 (to run, jump, ...))
- 흘러들다 (흐르다 (to flow))
- 날아들다 (날다 (to fly))
- 모여들다 (모이다 (to gather))
- 스며들다 (스미다 (to seep))
- 줄어들다 (줄다 (to decrease))