Luka is gay, not trans. He dresses like a woman not because he wants to but because he's been pressured into it by an abusive family (his father and big sister). And he doesn't really want to be a woman either, though he claims to. Instead, what he truly wants is to be in a romantic relationship with Okabe, who he is madly in love with. But he sees romance between men as something society (and himself, possibly) won't ever accept, so if turning himself into a woman is what he needs to do to win Okabe's love, he'll take it.
Basically, Luka does not feel like a woman trapped in a man's body, nor does he suffer from gender dysphoria. He is simply gay and struggles with his own homophobia, reaching for the "simple solution" when it is presented to him.
I absolutely do believe that the creators wanted Luka to be a story about a trans person, but they seem to have had little to no understanding of the concept before writing it. In general, the Science Adventure series has a problem with transphobia, especially visible in Occultic;Nine and Anonymous;Code.
Disclaimer: I'm neither gay nor trans, so I'm not exactly coming at this from a position of authority. The whole thing is somewhat open to interpretation, but the more I've seen and read of Steins;Gate, the more confident I feel in the stuff I wrote above.