You sure know how to misunderstand simple things.
It's (1). Full stop. Stop trying to make imaginary logical chains. You can only say if (1), then (2) the usage of gay to mean homosexual is illegitimate.
That's all.
Regarding your opening expression of what I have said, your misunderstanding is thinking I have been saying that a word must mean exactly and only the precise definition of what it once meant (which is what you are implying I mean here, which IS absurd, and I do not mean that).
I do mean that legitimate use is linked to the original meaning. A thread connecting it to the idea of merriment would remain. And it doesn't. There is no such thread, therefore the use is illegitimate. That is why you inserted question marks in your own imagination of my chain.
While we are called to be wise as serpents, we are also called to become like little children if we want to enter the Kingdom of Heaven. If your reason offends you, cut it off! (And by "offend", I don't mean "disgust" or "anger", but "interferes with accepting the truth of Holy Tradition", here, that the Christian ideal is just as eternal in sexual morality as in everything else.
It's not hard. Maybe you would only need to be ten years older to see it, to remember when "gay" really did mean "merry", and how the word was hijacked for the express purpose of attaining social approval of the sin, which it has with a vengeance, and how now no one dares to use "gay" in its traditional meaning. A beautiful word has been ruined. (In Russian, that beautiful word is the word for "sky-blue".)
There's no long argument. It's not a complicated reasoning chain. It is as simple as 2+2=4. You have to make an effort to make it hard.