Translation:I like going shopping.
Is just 'shopping' instead of 'going shopping' not an acceptable translation for かいものに行く？
かいもの already means "shopping" but is a noun not a verb so i guess this is their way to differentiate.
Is it really necessary to turn the 行く into a 行くの? I mean, "shopping" was already turned into a noun. What am I missing here?
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]"
I think its ok. Its not a direct translation but it has the same meaning. And to me, 'I like shopping' sounds more natural. Also to go can be omitted by implication. I.e. when you are shopping its implied that you have gone somewhere to shop