Grammatically it should be the first—homo and intraturus enclose mundi, and therefore the genitive belongs to them. This is a very common way of showing relationships between dependent words.
However, if it is true that Linnaeus meant the latter, then I'd offer that this isn't the best Latin. The A1B2A2B1 structure doesn't feel like proper Latin.
This sort of distance is possible with gentive hyperbaton, but from the examples that Devine adduces in his Latin Word Order (Oxford, 2006), this one does not seem to fit in. The parallel in English he gives for genitive hyperbaton is:
A critique hit the newstands of the Prime Minister's foreign policy.
Readers easily understand that these are not newstands of foreign policy, but rather that genitive goes with 'critique'. Indeed, in most of his examples, the genitive is separated from what it modifies by a verb ("contionem advocat militum", BC 2.32; "nemo inclamavit patronorum", De Orat. 1.230). He explains (with the example sensibus carebit oculorum):
[In genitive hyperbaton] the cofocus is a single pragmatically uniform syntactic constituent. The syntax is massaged to provide for a simple and direct translation into a pragmatically structured meaning.
This isn't always the case, though. Take these four examples:
tantum civitati Haeduae dignitatis tribuebat (BG 5.7)
neque...pacis umquam apud vos mentionem feci (Livy 21.13.3)
There is still no ambiguity here, and despite the hyperbaton, there isn't alternation between elements that go together. The structure is more chiastic here. I'd wager we only see the odd alternation in poetry, or if we see it at all in prose, it's very rare.
So, all in all, the first translation is the more natural way of saying things, the second is the odd one.
If you wanted to force the odd one, simply put mundi after theatrum. If you wanted to make the first less ambiguous, Joonas' suggestions of an adjective instead of a genitive (which is excellent Latin) or a relative clause are both correct.