Translation:I like going shopping.
Yes. 買い物に行く by itself means "(I) go shopping". You have to turn that clause into a noun 買い物に行くの in order to use it within the larger sentence 私は[買い物に行くの]が好き "I like [to go shopping]".
The English sentence has something roughly similar. "I go shopping" is a complete sentence. But in order to use it within a larger sentence, as in to say that you like doing that, you have to change "I go" to either the infinitive "to go" or the gerund "going". So, "I go shopping" → "I like [going (or to go) shopping]". You can't simply stick "I go shopping" into the larger sentence, to make "I like [I go shopping]"