His story was of a driving desire, and certainly he had romantic notions that were satisfying in the moment, and still are in his reverie. But in the instance that he shows his ability to just walk away not minding that no more will come of it, he proves that he is not one.
Every definition I have found online so far, say the same thing. Hopeless romantics are in love with being in love. True love. The kind of fairytales. And they tend to fall hard and fast. I see no evidence of that in his little evening under the stars. There are romantic people and then there are hopeless romantics. There is definately a difference.