It's clearly expected that the answer is
although I don't think a fine line can be drawn. So I understand that the question can be confusing. It needs to be asked because some facts about syntax hold true invaruably of the semantics, and vice versa, so we want to disambiguate. Specifically:
The reader needs to apply sentence level syntax to find the verbs corresponding to each occasion of "they". Then it's a matter of semantics to understand what agent could fulfill that verb, and a matter of text-level syntax to find the nearest noun that can fulfill that role.
Sodas don't possess anything, so the second occasion of "they", that is "they didn't have many snacks available", must refer to something else. What else? Well, that's not really a matter of syntax for various reasons. One could conclude that backtracking is not a sentence-syntactic operation and chalk it up to pragmatics and context. One could also say that part of the semantics of they is introducing indefinite subjects. That is, we haven't even been told who threw the party.
PS: Although the word "party" derives from the description of a group of people that usually has a leader, semantics only can extract this throug contextual inference, in which syntactic production only plays a minor role, covering the meaning up under an adverb of place, "at the party", that is commanded by the verb of movement, arrive. The referent of the indefinite pronoun is hidden in the text-level semantics and needs to be extracted semantically.
PPS: Also, as a metter of semantics, we can tell from the negative polarity item, "didn't", that it doesn't matter who did not provide for many snacks: Nobody had many available for the speaker. We later infer that they had chips, but we don't really care who, as far as syntax is concerned. Thus we merely infer through syntax, that I ate chips at the party.
What's more, I'm not sure, but I'd guess in a regional jocular "I ate me some chips" there's a mediopassive. The chips are their own, not mine or anyones. Only through eating do they become a part of me. The category does not make much sense for English, though, because the verbs are not morphemically inflected.
Hope I didn't confuse.