I would consider both interpretations equally valid. If anything, in law we have the "rule of the last antecedent" (phrase/clause modifies nearest antecedent noun) so that the hater's interpretation could be more correct if based only on this rule.
This language is ambiguous: "host ... opens another door, say #3, which has a goat."
The two options are Marilyn's interpretation of the door always containing a goat (invariant version), or that one door he opens (say #3) just happens to contain a goat (hater's version) but it could have contained a car.
As suggested by someone below, a much clearer formation could have said "host opens a door with a goat, say door #3" to avoid this particular ambiguity.
There's also the issue of usage of "which" signifying a non-restrictive non-essential clause.