Aha, no, not romantic in that case. Implication was closer to familial.
Dovahkin has motivation to stick around at first because:
1. He needs to learn the language and buff up on local lore. No instant plot-device accidental translation spell, because he won't be pissing Louise off with incessant chatter.
2. The need to work out the complexities of political, social, and magical norms so that he doesn't end up screwing himself. He's summoned to a school, the school has a big library.
3. Once he realizes that the summoning a) wasn't related in any way to Conjuration or the Dovah-summoning Thu'um, and b) has taken him outside of Mundus, he's got motivation to stick around to study the cause of it, both because it's likely his best chance of finding a way back and because anything with enough power to pull someone from Mundus into another material dimension is probably going to be related in some way to the underlying nature of the universe as the scholars of Nirn know it.
4. Once the hints about Louise being a Void mage start coming, that's a red flag. The guy is first and foremost seeking knowledge, beyond even his goals in the Empire. If he has a pre-existing relationship with a mortal who could potentially be carrying a shard of the power of the deity/entity that carved a new plane of existence out of the Void, there's no way in hell he's abandoning that.
Remember, the path he's trying to follow to achieve CHIM is an investigation into the respective natures of the Night Mother, Sithis (who is more-or-less considered to be Padomay, one of the two brothers born of the Void; Sithis is also said to send the souls he claims to the Void), and Lorkhan, who is considered to be the son of Padomay, and who is credited with both realizing CHIM and orchestrating the creation of Mundus. To the Dovahkin's mind, a direct link to Void could lead him to a greater understanding of the true nature of Sithis, and from there the same sort of understanding of Lorkhan, which might provide insight into achieving CHIM. As I said, the man realizes that it's almost certainly futile, but it's still a worthy goal.
That aside, according to his eventual hypothesis that Halkegenia is a new material plane carved from the Void and that Louise (and other Void mages) are somehow related to the creator of it, then that power is likely the best thing he'll find to a ticket back to Mundus.
So in short, he sticks around at first because he needs information, in the middle run because he has a study-buddy and a vast library of local lore (not to mention a young Dovah--both in the sense of it being an opportunity to instruct a dragon younger than himself who isn't beholden to Alduin, and because she represents a tangible link to Mundus, at least according to his assumption that Rhyme dragons are kin to Akatosh), and in the long run both because of a twofold opportunity to pursue his greatest ambition as well as a chance of returning to Mundus and his various lesser goals.
There may also be hints of an intent to try and permanently bridge Halkegenia and Mundus, because hey, he's been helping them deal with their problems, and his own homeland just so happens to have trouble with golden-haired pointy-eared fuckers with abnormal magical aptitude, and guess who the Brimiric peoples hate...