Hi Peter! Thanks for asking. Well, yes, it is the Holy Spirit that is meant by "spirit". I understand your question, since there are indeed bibleverses where "spirit" referes to our human spirit, which, next to our body and our soul, defines our individuality (cf. 1. Cor 2:11; Gal 6:18; Mt 26:41). The Hebrew word (ruach) and the Greek word (pneuma) are the same word that are also used for the Spirit of God and the Holy Spirit. The context has to be taken into consideration. 

Coming back to 1 John 3:24: Not only do we abide in God, but God also abides in us. How do we abide in Him (in God)? Well, in keeping His commandments, His expressed will. That is a characterizing condition of the Children of God. Then we have practical fellowship with God. In other words, we are obedient and do not sin. But God also abides in us. How do we know? Because He, that is God, has given us the Holy Spirit. God abides (stays) in us through the Holy Spirit. So, the Holy Spirit is the guarantee and proof that God abides in us. But that can only be said of the believer, the Child of God. Every human being has a spirit, even unbelievers. But here "spirit" is meant to be the seal that God abides in us, and this can only be said of a believer; hence, "spirit" has to be the Holy Spirit. Hope that helps!