Question: Trying to figure out the fallacy here, I can't put my thumb on it.

The claimant prefaces his or her statement with "I believe" which neutralizes the claim.
It is simply a statement of belief.

The belief states there are only two genders and thus
through its ambiguous use of the word, gender creates a Fallacy of Amphiboly.

Linguistically, an amphiboly is a type of ambiguity that results from ambiguous grammar, as opposed to one that results from the ambiguity of words or phrases—that is, equivocation. Logically, the fallacy of amphiboly occurs when a bad argument trades upon grammatical ambiguity to create an illusion of cogency.

As Dr. Bo describes:

Ambiguity Fallacy

(also known as: ambiguous assertion, amphiboly, amphibology, semantical ambiguity, vagueness)

Description: When an unclear phrase with multiple definitions is used within the argument; therefore, does not support the conclusion. Some will say single words count for the ambiguity fallacy, which is really a specific form of a fallacy known as equivocation.

Logical Form:

Claim X is made.

Y is concluded based on an ambiguous understanding of X.