It's easy to read this as Kirk not falling in love with anybody at all, but merely executing a clever campaign to defeat his foe. Just like he always does with the men and women he meets.
I never thought of that. It puts a wildly different spin on things. The question is, was the drama that sophisticated? The writing style of one-hour drama, in that period and well beyond, seldom did anything clever without some dialog to announce it during, and then put a button on it at the end.
But we can read into things, like you said.