It's sort of an interpreted term. In terms of Literature, romantic refers to the "Romantic Period" which, short short version, had alot to do with idealized situations and, oddly, conflicted heroes. The poetry of the time also had a focus on natural beauty.
So alot of themes located in here could be classically "romantic". Some have suggested that this "romantic fantasy" is the type championed by some of the popular female fantasy authors of the last 30 years or so: Lackey, et al.
The psychic furry friends angle plays into that, that's for sure. Y'know. Strong female characters, character-driven, psychic cute animals of some sort invariably turning up and bonding permanently in total sweet-and-light harmony. Big Bad Guys who are BAAAAD but minor bad guys who are charming and handsome and invariably seduce the heroine before betraying her utterly, yada yada.
I think they're overdoing it a tad, putting too many "romantic" elements in there. The beauty of nature, flowers (oh god, the flowers), the "Light" and "Shadow" alignments, basing nature off of Tarot cards, Psychic Furry Friends, the perfect natural splendor of the wonderful Kingdom where everybody gets along ... I'm waiting for rules on how to fall in love with handsomely evil foes before getting betrayed.
--fje